# Quiz 6: Continuous Probability Distributions

Statistics

Q 1Q 1

The center of a normal curve is
A) always equal to zero
B) is the mean of the distribution
C) cannot be negative
D) is the standard deviation

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Multiple Choice

B

Q 2Q 2

The probability that a continuous random variable takes any specific value
A) is equal to zero
B) is at least 0.5
C) depends on the probability density function
D) is very close to 1.0

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Multiple Choice

A

Q 3Q 3

A normal distribution with a mean of 0 and a standard deviation of 1 is called
A) a probability density function
B) an ordinary normal curve
C) a standard normal distribution
D) none of these alternatives is correct

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Multiple Choice

C

Q 4Q 4

The z score for the standard normal distribution
A) is always equal to zero
B) can never be negative
C) can be either negative or positive
D) is always equal to the mean

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Multiple Choice

Q 5Q 5

In a standard normal distribution, the probability that Z is greater than zero is
A) 0.5
B) equal to 1
C) at least 0.5
D) 1.96

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Multiple Choice

Q 6Q 6

A negative value of Z indicates that
A) the number of standard deviations of an observation is to the right of the mean
B) the number of standard deviations of an observation is to the left of the mean
C) a mistake has been made in computations, since Z cannot be negative
D) the data has a negative mean

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Multiple Choice

Q 7Q 7

The uniform, normal, and exponential distributions are
A) all continuous probability distributions
B) all discrete probability distributions
C) can be either continuous or discrete, depending on the data
D) all the same distributions

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Multiple Choice

Q 8Q 8

A value of 0.5 that is added and/or subtracted from a value of x when the continuous normal distribution is used to approximate the discrete binomial distribution is called
A) 50% of the area under the normal curve
B) continuity correction factor
C) factor of conversion
D) all of the alternatives are correct answers

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Multiple Choice

Q 9Q 9

For a continuous random variable x, the probability density function fx) represents
A) the probability at a given value of x
B) the area under the curve at x
C) the area under the curve to the right of x
D) the height of the function at x

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Multiple Choice

Q 10Q 10

The uniform probability distribution is used with
A) a continuous random variable
B) a discrete random variable
C) a normally distributed random variable
D) any random variable, as long as it is not nominal

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Multiple Choice

Q 11Q 11

For any continuous random variable, the probability that the random variable takes on exactly a specific value is
A) 1.00
B) 0.50
C) any value between 0 to 1
D) almost zero

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Multiple Choice

Q 12Q 12

For the standard normal probability distribution, the area to the left of the mean is
A) -0.5
B) 0.5
C) any value between 0 to 1
D) 1

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Multiple Choice

Q 13Q 13

Which of the following is not a characteristic of the normal probability distribution?
A) The mean, median, and the mode are equal
B) The mean of the distribution can be negative, zero, or positive
C) The distribution is symmetrical
D) The standard deviation must be 1

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Multiple Choice

Q 14Q 14

In a standard normal distribution, the range of values of z is from
A) minus infinity to infinity
B) -1 to 1
C) 0 to 1
D) -3.09 to 3.09

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Multiple Choice

Q 15Q 15

For a uniform probability density function,
A) the height of the function cannot be larger than one
B) the height of the function is the same for each value of x
C) the height of the function is different for various values of x
D) the height of the function decreases as x increases

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Multiple Choice

Q 16Q 16

The probability density function for a uniform distribution ranging between 2 and 6 is
A) 4
B) undefined
C) any positive value
D) 0.25

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Multiple Choice

Q 17Q 17

A uniform probability distribution is a continuous probability distribution where the probability that the random variable assumes a value in any interval of equal length is
A) different for each interval
B) the same for each interval
C) at least one
D) None of these alternatives is correct.

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Multiple Choice

Q 18Q 18

The function that defines the probability distribution of a continuous random variable is a
A) normal function
B) uniform function
C) either normal of uniform depending on the situation
D) probability density function

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Multiple Choice

Q 19Q 19

When a continuous probability distribution is used to approximate a discrete probability distribution
A) a value of 0.5 is added and/or subtracted from the area
B) a value of 0.5 is added and/or subtracted from the value of x
C) a value of 0.5 is added to the area
D) a value of 0.5 is subtracted from the area

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Multiple Choice

Q 20Q 20

A continuous probability distribution that is useful in describing the time, or space, between occurrences of an event is an)
A) normal probability distribution
B) uniform probability distribution
C) exponential probability distribution
D) Poisson probability distribution

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Multiple Choice

Q 21Q 21

The exponential probability distribution is used with
A) a discrete random variable
B) a continuous random variable
C) any probability distribution with an exponential term
D) an approximation of the binomial probability distribution

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Multiple Choice

Q 22Q 22

In a standard normal distribution the probability of z being less than or equal zero is
A) 0.0000
B) much larger than 1
C) there is no answer to this question, since the value of the mean is not known
D) 0.5000

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Multiple Choice

Q 23Q 23

Larger values of the standard deviation result in a normal curve that is
A) shifted to the right
B) shifted to the left
C) narrower and more peaked
D) wider and flatter

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Multiple Choice

Q 24Q 24

Which of the following is not a characteristic of the normal probability distribution?
A) symmetry
B) The total area under the curve is always equal to 1.
C) 99.72% of the time the random variable assumes a value within plus or minus 1 standard deviation of its mean
D) The mean is equal to the median, which is also equal to the mode.

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Multiple Choice

Q 25Q 25

For a normal distribution, a negative value of z indicates
A) a mistake has been made in computations, because z is always positive
B) the area corresponding to the z is negative
C) the z is to the left of the mean
D) the z is to the right of the mean

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Multiple Choice

Q 26Q 26

The mean of a standard normal probability distribution
A) is always equal to zero
B) can be any value as long as it is positive
C) can be any value
D) is always greater than zero

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Multiple Choice

Q 27Q 27

The standard deviation of a standard normal distribution
A) is always equal to zero
B) is always equal to one
C) can be any positive value
D) can be any value

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Multiple Choice

Q 28Q 28

A normal probability distribution
A) is a continuous probability distribution
B) is a discrete probability distribution
C) can be either continuous or discrete
D) must have a standard deviation of 1

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Multiple Choice

Q 29Q 29

A continuous random variable may assume
A) all values in an interval or collection of intervals
B) only integer values in an interval or collection of intervals
C) only fractional values in an interval or collection of intervals
D) all the positive integer values in an interval

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Multiple Choice

Q 30Q 30

If the mean of a normal distribution is negative,
A) the standard deviation must also be negative
B) the variance must also be negative
C) a mistake has been made in the computations, because the mean of a normal distribution cannot be negative
D) None of these alternatives is correct.

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Multiple Choice

Q 31Q 31

For a standard normal distribution, the probability of z ≤ 0 is
A) zero
B) -0.5
C) 0.5
D) one

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Multiple Choice

Q 32Q 32

The highest point of a normal curve occurs at
A) one standard deviation to the right of the mean
B) two standard deviations to the right of the mean
C) approximately three standard deviations to the right of the mean
D) the mean

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Multiple Choice

Q 33Q 33

The random variable x is known to be uniformly distributed between 70 and 90. The probability of x having a value between 80 to 95 is
A) 0.75
B) 0.5
C) 0.05
D) 1

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Multiple Choice

Q 34Q 34

Z is a standard normal random variable. The P-1.96 ≤ Z ≤ -1.4) equals
A) 0.8942
B) 0.0558
C) 0.475
D) 0.4192

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Multiple Choice

Q 35Q 35

A standard normal distribution is a normal distribution
A) with a mean of 1 and a standard deviation of 0
B) with a mean of 0 and a standard deviation of 1
C) with any mean and a standard deviation of 1
D) with any mean and any standard deviation

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Multiple Choice

Q 36Q 36

Z is a standard normal random variable. The P 1.20 ≤ Z ≤ 1.85) equals
A) 0.4678
B) 0.3849
C) 0.8527
D) 0.0829

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Multiple Choice

Q 37Q 37

Z is a standard normal random variable. The P -1.20 ≤ Z ≤ 1.50) equals
A) 0.0483
B) 0.3849
C) 0.4332
D) 0.8181

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Multiple Choice

Q 38Q 38

Given that Z is a standard normal random variable, what is the probability that -2.51 ≤ Z ≤ -1.53?
A) 0.4950
B) 0.4370
C) 0.0570
D) 0.9310

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Multiple Choice

Q 39Q 39

Given that Z is a standard normal random variable, what is the probability that Z ≥ -2.12?
A) 0.4830
B) 0.9830
C) 0.017
D) 0.966

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Multiple Choice

Q 40Q 40

Given that Z is a standard normal random variable, what is the probability that -2.08 ≤ Z ≤ 1.46?
A) 0.9091
B) 0.4812
C) 0.4279
D) 0.0533

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Multiple Choice

Q 41Q 41

In a standard normal distribution the value of z
A) can be any value
B) cannot be negative
C) cannot be larger than 3.09
D) cannot be larger than 0.50

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Multiple Choice

Q 42Q 42

Z is a standard normal random variable. The P 1.41 ≤ Z ≤ 2.85) equals
A) 0.4978
B) 0.4207
C) 0.9185
D) 0.0771

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Multiple Choice

Q 43Q 43

X is a normally distributed random variable with a mean of 8 and a standard deviation of 4. The probability that X is between 1.48 and 15.56 is
A) 0.0222
B) 0.4190
C) 0.5222
D) 0.9190

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Multiple Choice

Q 44Q 44

X is a normally distributed random variable with a mean of 5 and a variance of 4. The probability that X is greater than 10.52 is
A) 0.0029
B) 0.0838
C) 0.4971
D) 0.9971

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Multiple Choice

Q 45Q 45

X is a normally distributed random variable with a mean of 12 and a standard deviation of 3. The probability that X equals 19.62 is
A) 0.000
B) 0.0055
C) 0.4945
D) 0.9945

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Multiple Choice

Q 46Q 46

X is a normally distributed random variable with a mean of 22 and a standard deviation of 5. The probability that X is less than 9.7 is
A) 0.000
B) 0.4931
C) 0.0069
D) 0.9931

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Multiple Choice

Q 47Q 47

Given that Z is a standard normal random variable, what is the value of Z if the area to the right of Z is 0.5?
A) 0.0000
B) 1.0000
C) 0.1915
D) 0.3413

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Multiple Choice

Q 48Q 48

Use the normal approximation to the binomial distribution to answer this question. Fifteen percent of all students at a large university are absent on Mondays. If a random sample of 12 names is called on a Monday, what is the probability that four students are absent?
A) 0.0683
B) 0.0213
C) 0.0021
D) 0.1329

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Multiple Choice

Q 49Q 49

Given that Z is a standard normal random variable, what is the value of Z if the area to the left of Z is 0.0559?
A) 0.4441
B) 1.59
C) 0.0000
D) 1.50

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Multiple Choice

Q 50Q 50

An exponential probability distribution
A) is a continuous distribution
B) is a discrete distribution
C) can be either continuous or discrete
D) must be normally distributed

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Multiple Choice

Q 51Q 51

Z is a standard normal random variable. What is the value of Z if the area to the right of Z is 0.1112?
A) 0.3888
B) 1.22
C) 2.22
D) 3.22

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Multiple Choice

Q 52Q 52

Z is a standard normal random variable. What is the value of Z if the area between -Z and Z is 0.754?
A) 0.377
B) 0.123
C) 2.16
D) 1.16

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Multiple Choice

Q 53Q 53

Z is a standard normal random variable. What is the value of Z if the area to the right of Z is 0.9803?
A) -2.06
B) 0.4803
C) 0.0997
D) 3.06

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Multiple Choice

Q 54Q 54

For a standard normal distribution, the probability of obtaining a z value between -2.4 to -2.0 is
A) 0.4000
B) 0.0146
C) 0.0400
D) 0.5000

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Multiple Choice

Q 55Q 55

For a standard normal distribution, the probability of obtaining a z value of less than 1.6 is
A) 0.1600
B) 0.0160
C) 0.0016
D) 0.9452

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Multiple Choice

Q 56Q 56

For a standard normal distribution, the probability of obtaining a z value between -1.9 to 1.7 is
A) 0.9267
B) 0.4267
C) 1.4267
D) 0.5000

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Multiple Choice

Q 57Q 57

The ages of students at a university are normally distributed with a mean of 21. What percentage of the student body is at least 21 years old?
A) It could be any value, depending on the magnitude of the standard deviation
B) 50%
C) 21%
D) 1.96%

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Multiple Choice

Q 58Q 58

Z is a standard normal random variable. The P1.05 ≤ Z ≤ 2.13) equals
A) 0.8365
B) 0.1303
C) 0.4834
D) 0.3531

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Multiple Choice

Q 59Q 59

Z is a standard normal random variable. The PZ ≥ 2.11) equals
A) 0.4821
B) 0.9821
C) 0.5
D) 0.0174

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Multiple Choice

Q 60Q 60

The entire area under the standard normal distribution curve
A) can be any value
B) cannot be negative
C) can be any positive value
D) can be any positive value larger than 1

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Multiple Choice

Q 61Q 61

Z is a standard normal random variable. The P-1.5 ≤ Z ≤ 1.09) equals
A) 0.4322
B) 0.3621
C) 0.7953
D) 0.0711

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Multiple Choice

Q 62Q 62

Given that Z is a standard normal random variable. What is the value of Z if the area to the left of Z is 0.9382?
A) 1.8
B) 1.54
C) 2.1
D) 1.77

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Multiple Choice

Q 63Q 63

Given that Z is a standard normal random variable. What is the value of Z if the area to the right of Z is 0.1401?
A) 1.08
B) 0.1401
C) 2.16
D) -1.08

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Multiple Choice

Q 64Q 64

Given that Z is a standard normal random variable, what is the value of Z if the area to the right of Z is 0.9834?
A) 0.4834
B) -2.13
C) +2.13
D) zero

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Multiple Choice

Q 65Q 65

Given that Z is a standard normal random variable, what is the value of Z if the area to the left of Z is 0.119?
A) 0.381
B) +1.18
C) -1.18
D) 2.36

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Multiple Choice

Q 66Q 66

Given that Z is a standard normal random variable, what is the value of Z if the area between -Z and Z is 0.901?
A) 1.96
B) -1.96
C) 0.4505
D) ±1.65

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Multiple Choice

Q 67Q 67

In a standard normal distribution the value of z
A) can be any value
B) cannot be negative
C) cannot be larger than 3.09
D) cannot be larger than 0.50

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Multiple Choice

Q 68Q 68

Exhibit 6-1
The assembly time for a product is uniformly distributed between 6 to 10 minutes.
-Refer to Exhibit 6-1. The probability density function has what value in the interval between 6 and 10?
A) 0.25
B) 4.00
C) 5.00
D) zero

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Multiple Choice

Q 69Q 69

Exhibit 6-1
The assembly time for a product is uniformly distributed between 6 to 10 minutes.
-Refer to Exhibit 6-1. The probability of assembling the product between 7 to 9 minutes is
A) zero
B) 0.50
C) 0.20
D) 1

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Multiple Choice

Q 70Q 70

Exhibit 6-1
The assembly time for a product is uniformly distributed between 6 to 10 minutes.
-Refer to Exhibit 6-1. The probability of assembling the product in less than 6 minutes is
A) zero
B) 0.50
C) 0.15
D) 1

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Multiple Choice

Q 71Q 71

Exhibit 6-1
The assembly time for a product is uniformly distributed between 6 to 10 minutes.
-Refer to Exhibit 6-1. The probability of assembling the product in 7 minutes or more is
A) 0.25
B) 0.75
C) zero
D) 1

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Multiple Choice

Q 72Q 72

Exhibit 6-1
The assembly time for a product is uniformly distributed between 6 to 10 minutes.
-Refer to Exhibit 6-1. The expected assembly time in minutes) is
A) 16
B) 2
C) 8
D) 4

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Multiple Choice

Q 73Q 73

Exhibit 6-1
The assembly time for a product is uniformly distributed between 6 to 10 minutes.
-Refer to Exhibit 6-1. The standard deviation of assembly time in minutes) is approximately
A) 1.3333
B) 1.1547
C) 0.1111
D) 0.5773

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Multiple Choice

Q 74Q 74

Exhibit 6-2
The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds.
-Refer to Exhibit 6-2. The probability of a player weighing more than 241.25 pounds is
A) 0.4505
B) 0.0495
C) 0.9505
D) 0.9010

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Multiple Choice

Q 75Q 75

Exhibit 6-2
The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds.
-Refer to Exhibit 6-2. The probability of a player weighing less than 250 pounds is
A) 0.4772
B) 0.9772
C) 0.0528
D) 0.5000

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Multiple Choice

Q 76Q 76

Exhibit 6-2
The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds.
-Refer to Exhibit 6-2. What percent of players weigh between 180 and 220 pounds?
A) 28.81%
B) 0.5762%
C) 0.281%
D) 57.62%

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Multiple Choice

Q 77Q 77

Exhibit 6-2
The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds.
-Refer to Exhibit 6-2. What is the minimum weight of the middle 95% of the players?
A) 196
B) 151
C) 249
D) 190

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Multiple Choice

Q 78Q 78

Exhibit 6-3
Consider the continuous random variable X, which has a uniform distribution over the interval from 20 to 28.
-Refer to Exhibit 6-3. The probability density function has what value in the interval between 20 and 28?
A) 0
B) 0.050
C) 0.125
D) 1.000

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Multiple Choice

Q 79Q 79

Exhibit 6-3
Consider the continuous random variable X, which has a uniform distribution over the interval from 20 to 28.
-Refer to Exhibit 6-3. The probability that X will take on a value between 21 and 25 is
A) 0.125
B) 0.250
C) 0.500
D) 1.000

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Multiple Choice

Q 80Q 80

Exhibit 6-3
Consider the continuous random variable X, which has a uniform distribution over the interval from 20 to 28.
-Refer to Exhibit 6-3. The probability that X will take on a value of at least 26 is
A) 0.000
B) 0.125
C) 0.250
D) 1.000

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Multiple Choice

Q 81Q 81

Exhibit 6-3
Consider the continuous random variable X, which has a uniform distribution over the interval from 20 to 28.
-Refer to Exhibit 6-3. The mean of X is
A) 0.000
B) 0.125
C) 23
D) 24

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Multiple Choice

Q 82Q 82

Exhibit 6-3
Consider the continuous random variable X, which has a uniform distribution over the interval from 20 to 28.
-Refer to Exhibit 6-3. The variance of X is approximately
A) 2.309
B) 5.333
C) 32
D) 0.667

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Multiple Choice

Q 83Q 83

Exhibit 6-4
fx) =1/10) e-x/10 x ≥ 0
-Refer to Exhibit 6-4. The mean of x is
A) 0.10
B) 10
C) 100
D) 1,000

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Multiple Choice

Q 84Q 84

Exhibit 6-4
fx) =1/10) e-x/10 x ≥ 0
-Refer to Exhibit 6-4. The probability that x is between 3 and 6 is
A) 0.4512
B) 0.1920
C) 0.2592
D) 0.6065

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Multiple Choice

Q 85Q 85

Exhibit 6-4
fx) =1/10) e-x/10 x ≥ 0
-Refer to Exhibit 6-4. The probability that x is less than 5 is
A) 0.6065
B) 0.0606
C) 0.3935
D) 0.9393

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Multiple Choice

Q 86Q 86

Exhibit 6-5
The travel time for a college student traveling between her home and her college is uniformly distributed between 40 and 90 minutes.
-Refer to Exhibit 6-5. The probability that she will finish her trip in 80 minutes or less is
A) 0.02
B) 0.8
C) 0.2
D) 1.00

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Multiple Choice

Q 87Q 87

Exhibit 6-5
The travel time for a college student traveling between her home and her college is uniformly distributed between 40 and 90 minutes.
-Refer to Exhibit 6-5. The probability that her trip will take longer than 60 minutes is
A) 1.00
B) 0.40
C) 0.02
D) 0.600

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Multiple Choice

Q 88Q 88

Exhibit 6-5
The travel time for a college student traveling between her home and her college is uniformly distributed between 40 and 90 minutes.
-Refer to Exhibit 6-5. The probability that her trip will take exactly 50 minutes is
A) zero
B) 0.02
C) 0.06
D) 0.20

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Multiple Choice

Q 89Q 89

Exhibit 6-6
The starting salaries of individuals with an MBA degree are normally distributed with a mean of $40,000 and a standard deviation of $5,000.
-Refer to Exhibit 6-6. What is the probability that a randomly selected individual with an MBA degree will get a starting salary of at least $30,000?
A) 0.4772
B) 0.9772
C) 0.0228
D) 0.5000

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Multiple Choice

Q 90Q 90

Exhibit 6-6
The starting salaries of individuals with an MBA degree are normally distributed with a mean of $40,000 and a standard deviation of $5,000.
-Refer to Exhibit 6-6. What is the probability that a randomly selected individual with an MBA degree will get a starting salary of at least $47,500?
A) 0.4332
B) 0.9332
C) 0.0668
D) 0.5000

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Multiple Choice

Q 91Q 91

Exhibit 6-6
The starting salaries of individuals with an MBA degree are normally distributed with a mean of $40,000 and a standard deviation of $5,000.
-Refer to Exhibit 6-6. What percentage of MBA's will have starting salaries of $34,000 to $46,000?
A) 38.49%
B) 38.59%
C) 50%
D) 76.98%

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Multiple Choice

Q 92Q 92

Exhibit 6-7
The weight of items produced by a machine is normally distributed with a mean of 8 ounces and a standard deviation of 2 ounces.
-Refer to Exhibit 6-7. What is the probability that a randomly selected item will weigh more than 10 ounces?
A) 0.3413
B) 0.8413
C) 0.1587
D) 0.5000

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Multiple Choice

Q 93Q 93

Exhibit 6-7
The weight of items produced by a machine is normally distributed with a mean of 8 ounces and a standard deviation of 2 ounces.
-Refer to Exhibit 6-7. What is the probability that a randomly selected item will weigh between 11 and 12 ounces?
A) 0.4772
B) 0.4332
C) 0.9104
D) 0.0440

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Multiple Choice

Q 94Q 94

Exhibit 6-7
The weight of items produced by a machine is normally distributed with a mean of 8 ounces and a standard deviation of 2 ounces.
-Refer to Exhibit 6-7. What percentage of items will weigh at least 11.7 ounces?
A) 46.78%
B) 96.78%
C) 3.22%
D) 53.22%

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Multiple Choice

Q 95Q 95

Exhibit 6-7
The weight of items produced by a machine is normally distributed with a mean of 8 ounces and a standard deviation of 2 ounces.
-Refer to Exhibit 6-7. What percentage of items will weigh between 6.4 and 8.9 ounces?
A) 0.1145
B) 0.2881
C) 0.1736
D) 0.4617

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Multiple Choice

Q 96Q 96

Exhibit 6-7
The weight of items produced by a machine is normally distributed with a mean of 8 ounces and a standard deviation of 2 ounces.
-Refer to Exhibit 6-7. What is the probability that a randomly selected item weighs exactly 8 ounces?
A) 0.5
B) 1.0
C) 0.3413
D) 0.0000

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Multiple Choice

Q 97Q 97

Exhibit 6-8
The life expectancy of a particular brand of tire is normally distributed with a mean of 40,000 and a standard deviation of 5,000 miles.
-Refer to Exhibit 6-8. What is the probability that a randomly selected tire will have a life of at least 30,000 miles?
A) 0.4772
B) 0.9772
C) 0.0228
D) 0.5000

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Multiple Choice

Q 98Q 98

Exhibit 6-8
The life expectancy of a particular brand of tire is normally distributed with a mean of 40,000 and a standard deviation of 5,000 miles.
-Refer to Exhibit 6-8. What is the probability that a randomly selected tire will have a life of at least 47,500 miles?
A) 0.4332
B) 0.9332
C) 0.0668
D) 0.4993

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Multiple Choice

Q 99Q 99

Exhibit 6-8
The life expectancy of a particular brand of tire is normally distributed with a mean of 40,000 and a standard deviation of 5,000 miles.
-Refer to Exhibit 6-8. What percentage of tires will have a life of 34,000 to 46,000 miles?
A) 38.49%
B) 76.98%
C) 50%
D) 88.49%

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Multiple Choice

Q 100Q 100

Exhibit 6-8
The life expectancy of a particular brand of tire is normally distributed with a mean of 40,000 and a standard deviation of 5,000 miles.
-Refer to Exhibit 6-8. What is the probability that a randomly selected tire will have a life of exactly 47,500 miles?
A) 0.0000
B) 0.9332
C) 0.0668
D) 0.4993

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Multiple Choice

Q 101Q 101

Exhibit 6-9
The average price of personal computers manufactured by MNM Company is $1,200 with a standard deviation of
$220. Furthermore, it is known that the computer prices manufactured by MNM are normally distributed.
-Refer to Exhibit 6-9. What is the probability that a randomly selected computer will have a price of at least $1,530?
A) 0.0668
B) 0.5668
C) 0.4332
D) 1.4332

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Multiple Choice

Q 102Q 102

Exhibit 6-9
The average price of personal computers manufactured by MNM Company is $1,200 with a standard deviation of
$220. Furthermore, it is known that the computer prices manufactured by MNM are normally distributed.
-Refer to Exhibit 6-9. Computers with prices of more than $1,750 receive a discount. What percentage of the computers will receive the discount?
A) 62%
B) 0.62%
C) 0.062%
D) 99.38%

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Multiple Choice

Q 103Q 103

Exhibit 6-9
The average price of personal computers manufactured by MNM Company is $1,200 with a standard deviation of
$220. Furthermore, it is known that the computer prices manufactured by MNM are normally distributed.
-Refer to Exhibit 6-9. What is the minimum value of the middle 95% of computer prices?
A) $1,768.80
B) $1,295.80
C) $2,400.00
D) $768.80

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Multiple Choice

Q 104Q 104

Exhibit 6-9
The average price of personal computers manufactured by MNM Company is $1,200 with a standard deviation of
$220. Furthermore, it is known that the computer prices manufactured by MNM are normally distributed.
-Refer to Exhibit 6-9. If 513 of the MNM computers were priced at or below $647.80, how many computers were produced by MNM?
A) 185,500
B) 85,500
C) 513,000
D) not enough information is provided to answer this question

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Multiple Choice

Q 105Q 105

Exhibit 6-10
A professor at a local university noted that the grades of her students were normally distributed with a mean of 73 and a standard deviation of 11.
-Refer to Exhibit 6-10. The professor has informed us that 7.93 percent of her students received grades of A. What is the minimum score needed to receive a grade of A?
A) 90.51
B) 93.2
C) 88.51
D) 100.00

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Multiple Choice

Q 106Q 106

Exhibit 6-10
A professor at a local university noted that the grades of her students were normally distributed with a mean of 73 and a standard deviation of 11.
-Refer to Exhibit 6-10. Students who made 57.93 or lower on the exam failed the course. What percent of students failed the course?
A) 8.53%
B) 18.53%
C) 91.47%
D) 0.853%

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Multiple Choice

Q 107Q 107

Exhibit 6-10
A professor at a local university noted that the grades of her students were normally distributed with a mean of 73 and a standard deviation of 11.
-Refer to Exhibit 6-10. If 69.5 percent of the students received grades of C or better, what is the minimum score of those who received C's?
A) 70.39
B) 67.39
C) 50.39
D) 65.39

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Multiple Choice

Q 108Q 108

The average price of cell phones manufactured by Ahmadi, Inc. is $98 with a standard deviation of $12. Furthermore, it is known that the prices of the cell phones manufactured by Ahmadi are normally distributed.
a. What percentage of cell phones produced by Ahmadi, Inc. will have prices of at least $120.20?
b. Cell phones with prices of at least 81.80 will get a free gift. What percentage of the cell phones will be eligible for the free gift?
c. What are the minimum and the maximum values of the middle 95% of cell phone prices?
d. If 7,218 of the Ahmadi cell phones were priced at least $119.00, how many cell phones were produced by Ahmadi, Inc.?

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Q 109Q 109

The driving time for an individual from his home to his work is uniformly distributed between 300 to 480 seconds.
a. Determine the probability density function.
b. Compute the probability that the driving time will be less than or equal to 435 seconds.
c. Determine the expected driving time.
d. Compute the variance.
e. Compute the standard deviation.

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Q 110Q 110

The Body Paint, an automobile body paint shop, has determined that the painting time of automobiles is uniformly distributed and that the required time ranges between 45 minutes to 1 hours.
a. Give a mathematical expression for the probability density function.
b. What is the probability that the painting time will be less than or equal to one hour?
c. What is the probability that the painting time will be more than 50 minutes?
d. Determine the expected painting time and its standard deviation.

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Q 111Q 111

For a standard normal distribution, determine the probabilities of obtaining the following z values. It is helpful to draw a normal distribution for each case and show the corresponding area.
a. Greater than zero
b. Between -2.4 and -2.0
c. Less than 1.6
d. Between -1.9 to 1.7
e. Between 1.5 and 1.75

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Q 112Q 112

A professor at a local community college noted that the grades of his students were normally distributed with a mean of 74 and a standard deviation of 10. The professor has informed us that 6.3 percent of his students received A's while only 2.5 percent of his students failed the course and received F's.
a. What is the minimum score needed to make an A?
b. What is the maximum score among those who received an F?
c. If there were 5 students who did not pass the course, how many students took the course?

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Q 113Q 113

The time it takes to hand carve a guitar neck is uniformly distributed between 110 and 190 minutes.
a. What is the probability that a guitar neck can be carved between 95 and 165 minutes?
b. What is the probability that the guitar neck can be carved between 120 and 200 minutes?
c. Determine the expected completion time for carving the guitar neck.
d. Compute the standard deviation.

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Q 114Q 114

Scores on a recent national statistics exam were normally distributed with a mean of 80 and a standard deviation of 6.
a. What is the probability that a randomly selected exam will have a score of at least 71?
b. What percentage of exams will have scores between 89 and 92?
c. If the top 2.5% of test scores receive merit awards, what is the lowest score eligible for an award?
d. If there were 334 exams with scores of at least 89, how many students took the exam?

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Q 115Q 115

The average starting salary of this year's MBA students is $35,000 with a standard deviation of $5,000. Furthermore, it is known that the starting salaries are normally distributed. What are the minimum and the maximum starting salaries of the middle 95% of MBA graduates?

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Short Answer

Q 116Q 116

The average starting salary for this year's graduates at a large university LU) is $20,000 with a standard deviation of $8,000. Furthermore, it is known that the starting salaries are normally distributed.
a. What is the probability that a randomly selected LU graduate will have a starting salary of at least $30,400?
b. Individuals with starting salaries of less than $15,600 receive a low income tax break. What percentage of the graduates will receive the tax break?
c. What are the minimum and the maximum starting salaries of the middle 95% of the LU graduates?
d. If 189 of the recent graduates have salaries of at least $32,240, how many students graduated this year from this university?

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Q 117Q 117

"DRUGS R US" is a large manufacturer of various kinds of liquid vitamins. The quality control department has noted that the bottles of vitamins marked 6 ounces vary in content with a standard deviation of 0.3 ounces. Assume the contents of the bottles are normally distributed.
a. What percentage of all bottles produced contains more than 6.51 ounces of vitamins?
b. What percentage of all bottles produced contains less than 5.415 ounces?
c. What percentage of bottles produced contains between 5.46 to 6.495 ounces?
d. Ninety-five percent of the bottles will contain at least how many ounces?
e. What percentage of the bottles contains between 6.3 and 6.6 ounces?

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Q 118Q 118

The Globe Fishery packs shrimp that weigh more than 1.91 ounces each in packages marked" large" and shrimp that weigh less than 0.47 ounces each into packages marked "small"; the remainder are packed in "medium" size packages. If a day's catch showed that 19.77 percent of the shrimp were large and 6.06 percent were small, determine the mean and the standard deviation for the shrimp weights. Assume that the shrimps' weights are normally distributed.

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Short Answer

Q 119Q 119

The monthly earnings of computer programmers are normally distributed with a mean of $4,000. If only 1.7 percent of programmers have monthly incomes of less than $2,834, what is the value of the standard deviation of the monthly earnings of the computer programmers?

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Short Answer

Q 120Q 120

A major department store has determined that its customers charge an average of $500 per month, with a standard deviation of $80. Assume the amounts of charges are normally distributed.
a. What percentage of customers charges more than $380 per month?
b. What percentage of customers charges less than $340 per month?
c. What percentage of customers charges between $644 and $700 per month?

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Q 121Q 121

The First National Mortgage Company has noted that 6% of its customers pay their mortgage payments after the due date.
a. What is the probability that in a random sample of 150 customers 7 will be late on their payments?
b. What is the probability that in a random sample of 150 customers at least 10 will be late on their payments?

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Q 122Q 122

The salaries of the employees of a corporation are normally distributed with a mean of $25,000 and a standard deviation of $5,000.
a. What is the probability that a randomly selected employee will have a starting salary of at least
$31,000?
b. What percentage of employees has salaries of less than $12,200?
c. What are the minimum and the maximum salaries of the middle 95% of the employees?
d. If sixty-eight of the employees have incomes of at least $35,600, how many individuals are employed in the corporation?

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Q 123Q 123

A manufacturing process produces items whose weights are normally distributed. It is known that 22.57% of all the items produced weigh between 100 grams up to the mean and 49.18% weigh from the mean up to 190 grams. Determine the mean and the standard deviation.

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Short Answer

Q 124Q 124

The daily dinner bills in a local restaurant are normally distributed with a mean of $28 and a standard deviation of
$6.
a. What is the probability that a randomly selected bill will be at least $39.10?
b. What percentage of the bills will be less than $16.90?
c. What are the minimum and maximum of the middle 95% of the bills?
d. If twelve of one day's bills had a value of at least $43.06, how many bills did the restaurant collect on that day?

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Q 125Q 125

The price of a bond is uniformly distributed between $80 and $85.
a. What is the probability that the bond price will be at least $83?
b. What is the probability that the bond price will be between $81 to $90?
c. Determine the expected price of the bond.
d. Compute the standard deviation for the bond price.

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Q 126Q 126

The price of a stock is uniformly distributed between $30 and $40.
a. What is the probability that the stock price will be more than $37?
b. What is the probability that the stock price will be less than or equal to $32?
c. What is the probability that the stock price will be between $34 and $38?
d. Determine the expected price of the stock.
e. Determine the standard deviation for the stock price.

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Q 127Q 127

A random variable X is uniformly distributed between 45 and 150.
a. Determine the probability of X = 48.
b. What is the probability of X ≤ 60?
c. What is the probability of X ≥ 50?
d. Determine the expected vale of X and its standard deviation.

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Q 128Q 128

The length of time patients must wait to see a doctor in a local clinic is uniformly distributed between 15 minutes and 2 1/2 hours.
a. What is the probability of a patient waiting exactly 50 minutes?
b. What is the probability that a patient would have to wait between 45 minutes and 2 hours?
c. Compute the probability that a patient would have to wait over 2 hours.
d. Determine the expected waiting time and its standard deviation.

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Q 129Q 129

The monthly income of residents of Daisy City is normally distributed with a mean of $3000 and a standard deviation of $500.
a. The mayor of Daisy City makes $2,250 a month. What percentage of Daisy City's residents has incomes that are more than the mayor's?
b. Individuals with incomes of less than $1,985 per month are exempt from city taxes. What percentage of residents is exempt from city taxes?
c. What are the minimum and the maximum incomes of the middle 95% of the residents?
d. Two hundred residents have incomes of at least $4,440 per month. What is the population of Daisy City?

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Q 130Q 130

The length of time it takes students to complete a statistics examination is uniformly distributed and varies between 40 and 60 minutes.
a. Find the mathematical expression for the probability density function.
b. Compute the probability that a student will take between 45 and 50 minutes to complete the examination.
c. Compute the probability that a student will take no more than 40 minutes to complete the examination.
d. What is the expected amount of time it takes a student to complete the examination?
e. What is the variance for the amount of time it takes a student to complete the examination?

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Q 131Q 131

The advertised weight on a can of soup is 10 ounces. The actual weight in the cans follows a uniform distribution and varies between 9.3 and 10.3 ounces.
a. Give the mathematical expression for the probability density function.
b. What is the probability that a can of soup will have between 9.4 and 10.3 ounces?
c. What is the mean weight of a can of soup?
d. What is the standard deviation of the weight?

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Q 132Q 132

The miles-per-gallon obtained by the 1995 model Z cars is normally distributed with a mean of 22 miles-per-gallon and a standard deviation of 5 miles-per-gallon.
a. What is the probability that a car will get between 13.35 and 35.1 miles-per-gallon?
b. What is the probability that a car will get more than 29.6 miles-per-gallon?
c. What is the probability that a car will get less than 21 miles-per-gallon?
d. What is the probability that a car will get exactly 22 miles-per-gallon?

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Q 133Q 133

The salaries at a corporation are normally distributed with an average salary of $19,000 and a standard deviation of
$4,000.
a. What is the probability that an employee will have a salary between $12,520 and $13,480?
b. What is the probability that an employee will have a salary more than $11,880?
c. What is the probability that an employee will have a salary less than $28,440?

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Q 134Q 134

The monthly earnings of computer systems analysts are normally distributed with a mean of $4,300. If only 1.07 percent of the systems analysts have a monthly income of more than $6,140, what is the value of the standard deviation of the monthly earnings of the computer systems analysts?

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Short Answer

Q 135Q 135

A major credit card company has determined that its customers charge an average of $280 per month on their accounts with a standard deviation of $20.
a. What percentage of the customers charges more than $275 per month?
b. What percentage of the customers charges less than $243 per month?
c. What percentage of the customers charges between $241 and $301.60 per month?

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Q 136Q 136

The ticket sales for events held at the new civic center are believed to be normally distributed with a mean of 12,000 and a standard deviation of 1,000.
a. What is the probability of selling more than 10,000 tickets?
b. What is the probability of selling between 9,500 and 11,000 tickets?
c. What is the probability of selling more than 13,500 tickets?

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Q 137Q 137

In a normal distribution, it is known that 27.34% of all the items are included from 100 up to the mean, and another 45.99% of all the items are included from the mean up to 145. Determine the mean and the standard deviation of the distribution.

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Short Answer

Q 138Q 138

The records show that 8% of the items produced by a machine do not meet the specifications. Use the normal approximation to the binomial distribution to answer the following questions. What is the probability that a sample of 100 units contains
a. Five or more defective units?
b. Ten or fewer defective units?
c. Eleven or less defective units?

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Q 139Q 139

Approximate the following binomial probabilities by the use of normal approximation.
a. Px ≤ 12, n = 50, p = 0.3)
b. P12 ≤ x ≤ 18, n = 50, p = 0.3)

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Q 140Q 140

An airline has determined that 20% of its international flights are not on time. Use the normal approximation to the binomial distribution to answer the following questions. What is the probability that of the next 80 international flights
a. Fifteen or less will not be on time?
b. Eighteen or more will not be on time?
c. Exactly 17 will not be on time?

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Q 141Q 141

The time it takes a mechanic to change the oil in a car is exponentially distributed with a mean of 5 minutes.
a. What is the probability density function for the time it takes to change the oil?
b. What is the probability that it will take a mechanic less than 6 minutes to change the oil?
c. What is the probability that it will take a mechanic between 3 and 5 minutes to change the oil?
d. What is the variance of the time it takes to change the oil?

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Q 142Q 142

The time it takes a worker on an assembly line to complete a task is exponentially distributed with a mean of 8 minutes.
a. What is the probability density function for the time it takes to complete the task?
b. What is the probability that it will take a worker less than 4 minutes to complete the task?
c. What is the probability that it will take a worker between 6 and 10 minutes to complete the task?

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Q 143Q 143

For a standard normal distribution, determine the probability of obtaining a Z value of
a. greater than zero.
b. between -2.34 to -2.55
c. less than 1.86.
d. between -1.95 to 2.7.
e. between 1.5 to 2.75.

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Q 144Q 144

The weights of items produced by a company are normally distributed with a mean of 4.5 ounces and a standard deviation of 0.3 ounces.
a. What is the probability that a randomly selected item from the production will weigh at least
4.14 ounces?
b. What percentage of the items weigh between 4.8 to 5.04 ounces?
c. Determine the minimum weight of the heaviest 5% of all items produced.
d. If 27,875 of the items of the entire production weigh at least 5.01 ounces, how many items have been produced?

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Q 145Q 145

The life expectancy of Timely brand watches is normally distributed with a mean of four years and a standard deviation of eight months.
a. What is the probability that a randomly selected watch will be in working condition for more than five years?
b. The company has a three-year warranty period on their watches. What percentage of their watches will be in operating condition after the warranty period?
c. What is the minimum and the maximum life expectancy of the middle 95% of the watches?
d. Ninety-five percent of the watches will have a life expectancy of at least how many months?

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Q 146Q 146

The weights of the contents of cans of tomato sauce produced by a company are normally distributed with a mean of 8 ounces and a standard deviation of 0.2 ounces.
a. What percentage of all cans produced contain more than 8.4 ounces of tomato paste?
b. What percentage of all cans produced contain less than 7.8 ounces?
c. What percentage of cans contains between 7.4 and 8.2 ounces?
d. Ninety-five percent of cans will contain at least how many ounces?
e. What percentage of cans contains between 8.2 and 8.4 ounces?

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Q 147Q 147

A professor at a local university noted that the grades of her students were normally distributed with a mean of 78 and a standard deviation of 10.
a. The professor has informed us that 16.6 percent of her students received grades of A. What is the minimum score needed to receive a grade of A?
b. If 12.1 percent of her students failed the course and received F's, what was the maximum score among those who received an F?
c. If 33 percent of the students received grades of B or better i.e., A's and B's), what is the minimum score of those who received a B?

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Q 148Q 148

In grading eggs into small, medium, and large, the Nancy Farms packs the eggs that weigh more than 3.6 ounces in packages marked "large" and the eggs that weigh less than 2.4 ounces into packages marked "small"; the remainder are packed in packages marked "medium." If a day's packaging contained 10.2% large and 4.18% small eggs, determine the mean and the standard deviation for the eggs' weights. Assume that the distribution of the weights is normal.

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Short Answer

Q 149Q 149

The weekly earnings of bus drivers are normally distributed with a mean of $395. If only 1.1 percent of the bus drivers have a weekly income of more than $429.35, what is the value of the standard deviation of the weekly earnings of the bus drivers?

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Short Answer

Q 150Q 150

A local bank has determined that the daily balances of the checking accounts of its customers are normally distributed with an average of $280 and a standard deviation of $20.
a. What percentage of its customers has daily balances of more than $275?
b. What percentage of its customers has daily balances less than $243?
c. What percentage of its customers' balances is between $241 and $301.60?

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Q 151Q 151

The contents of soft drink bottles are normally distributed with a mean of twelve ounces and a standard deviation of one ounce.
a. What is the probability that a randomly selected bottle will contain more than ten ounces of soft drink?
b. What is the probability that a randomly selected bottle will contain between 9.5 and 11 ounces?
c. What percentage of the bottles will contain less than 10.5 ounces of soft drink?

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Q 152Q 152

The time between arrivals of customers at the drive-up window of a bank follows an exponential probability distribution with a mean of 10 minutes.
a. What is the probability that the arrival time between customers will be 7 minutes or less?
b. What is the probability that the arrival time between customers will be between 3 and 7 minutes?

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Q 153Q 153

The time required to assemble a part of a machine follows an exponential probability distribution with a mean of 14 minutes.
a. What is the probability that the part can be assembled in 7 minutes or less?
b. What is the probability that the part can be assembled between 3.5 and 7 minutes?

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Q 154Q 154

The time it takes to completely tune an engine of an automobile follows an exponential distribution with a mean of 40 minutes.
a. What is the probability of tuning an engine in 30 minutes or less?
b. What is the probability of tuning an engine between 30 and 35 minutes?

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Q 155Q 155

The life expectancy of computer terminals is normally distributed with a mean of 4 years and a standard deviation of 10 months.
a. What is the probability that a randomly selected terminal will last more than 5 years?
b. What percentage of terminals will last between 5 and 6 years?
c. What percentage of terminals will last less than 4 years?
d. What percentage of terminals will last between 2.5 and 4.5 years?
e. If the manufacturer guarantees the terminals for 3 years and will replace them if they malfunction), what percentage of terminals will be replaced?

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Q 156Q 156

Approximate the following binomial probabilities by the use of normal approximation. Twenty percent of students who finish high school do not go to college. What is the probability that in a sample of 80 high school students
a. exactly 10 will not go to college?
b. 70 or more will go to college?
c. fourteen or fewer will not go to college?

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Q 157Q 157

The average life expectancy of dishwashers produced by a company is 6 years with a standard deviation of 8 month Assume that the lives of dishwashers are normally distributed.
a. What is the probability that a randomly selected dishwasher will have a life expectancy of at least 7 years?
b. Dishwashers that fail operating in less than 4 1/2 years will be replaced free of charge. What percent of dishwashers are expected to be replaced free of charge?
c. What are the minimum and the maximum life expectancy of the middle 95% of the dishwashers' lives? Give your answer in months.
d. If 155 of this year's dishwasher production fail operating in less than 4 years and 4 months, how many dishwashers were produced this year?

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Q 158Q 158

The average starting salary of this year's graduates of a large university LU) is $25,000 with a standard deviation
of $5,000. Furthermore, it is known that the starting salaries are normally distributed.
a. What is the probability that a randomly selected LU graduate will have a starting salary of at least $31,000?
b. Individuals with starting salaries of less than $12,200 receive a low income tax break. What
percentage of the graduates will receive the tax break?
c. What are the minimum and the maximum starting salaries of the middle 95% of the LU graduates?
d. If 68 of the recent graduates have salaries of at least $35,600, how many students graduated this year from this university?

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Q 159Q 159

The average starting salary of this year's graduates of a large university LU) is $20,000 with a standard deviation
of $8,000. Furthermore, it is known that the starting salaries are normally distributed.
a. What is the probability that a randomly selected LU graduate will have a starting salary of at least $30,400?
b. Individuals with starting salaries of less than $15,600 receive a low income tax break. What
percentage of the graduates will receive the tax break?
c. What are the minimum and the maximum starting salaries of the middle 95% of the LU graduates?
d. If 189 of the recent graduates have salaries of at least $32,240, how many students graduated this year from this university?

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Q 160Q 160

The SAT scores of students are normally distributed with a mean of 950 and a standard deviation of 200.
a. Nancy Bright's SAT score was 1390. What percentage of students have scores more than Nancy Bright?
b. What percentage of students score between 1100 and 1200?
c. What are the minimum and the maximum values of the middle 87.4% of the scores?
d. There were 165 students who scored above 1432. How many students took the SAT?

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Q 161Q 161

The prices of condos in a city are normally distributed with a mean of $90,000 and a standard deviation of $28,000.
a. The city government exempts the cheapest 6.68% of the condos from city taxes. What is the maximum price of the condos that will be exempt from city taxes?
b. If 1.79% of the most expensive condos are subject to a luxury tax, what is the minimum price of condos that will be subject to the luxury tax?

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Q 162Q 162

The Mathematics part of the SAT scores of students at UTC are normally distributed with a mean of 500 and a standard deviation of 75.
a. If 2.28 percent of the students who had the highest scores received scholarships, what was the minimum score among those who received scholarships? Do not round your answer.
b. It is known that 6.3 percent of students who applied to UTC were not accepted. What is the highest score of those who were denied acceptance? Do not round your answer.
c. What percentage of students had scores between 575 and 650?

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Q 163Q 163

The average life expectancy of computers produced by Ahmadi, Inc. is 6 years with a standard deviation of 10 months. Assume that the lives of computers are normally distributed. Suggestion: For this problem, convert ALL of the units to months.
a. What is the probability that a randomly selected computer will have a life expectancy of at least 7 years?
b. Computers that fail in less than 5 1/2 years will be replaced free of charge. What percentage
of computers are expected to be replaced free of charge?
c. What are the minimum and the maximum life expectancy of the middle 95% of the computers'
lives? Give your answers in months and do not round your answers.
d. The company is expecting that only 104 of this year's production will fail in less than 3 years and 8 months. How many computers were produced this year?

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