Question 1

Exhibit 6-1
Consider the continuous random variable x, which has a uniform distribution over the interval from 20 to 28.
-Refer to Exhibit 6-1. 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

Accepted Answer

The answer of Exhibit 6-1
Consider the continuous random variable x,...

Question 2

Exhibit 6-1
Consider the continuous random variable x, which has a uniform distribution over the interval from 20 to 28.
-Refer to Exhibit 6-1. The mean of x is
A)0.000
B)0.125
C)23
D)24

Accepted Answer

The answer of Exhibit 6-1
Consider the continuous random variable x,...

Question 3

Exhibit 6-2
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 6-2. The probability that her trip will take exactly 50 minutes is
A)zero
B)0.02
C)0.06
D)0.20

Accepted Answer

Since the travel time is uniformly distributed, the probability of any specific time (such as 50 minutes) occurring is equal to zero.

Question 4

Exhibit 6-1
Consider the continuous random variable x, which has a uniform distribution over the interval from 20 to 28.
-Refer to Exhibit 6-1. 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

Accepted Answer

The answer of Exhibit 6-1
Consider the continuous random variable x,...

Question 5

Exhibit 6-2
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 6-2. The probability that her trip will take longer than 60 minutes is
A)1.00
B)0.40
C)0.02
D)0.600

Accepted Answer

Since the distribution is uniform, the probability of the travel time being between 40 and 90 minutes is 1. The probability of it being longer than 60 minutes is the area of the shaded region in the diagram below, which is (90-60)/(90-40) = 30/50 = 0.6. Therefore, the answer is D.

![Exhibit 6-2 diagram](https://i.imgur.com/IXhjRyR.png)

Question 6

Exhibit 6-3
The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds.
-Refer to Exhibit 6-3. What percent of players weigh between 180 and 220 pounds?
A)34.13%
B)68.26%
C)0.3413%
D)None of the alternative answers is correct.

Accepted Answer

The answer of Exhibit 6-3
The weight of football players is...

Question 7

Exhibit 6-1
Consider the continuous random variable x, which has a uniform distribution over the interval from 20 to 28.
-Refer to Exhibit 6-1. 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

Accepted Answer

The probability of x being at least 26 is equal to the area under the probability density function to the right of 26. The total area under the uniform distribution is 1, and since the distribution is uniform, the probability density function is constant over the entire interval. Thus, the area to the right of 26 is (28-26)/(28-20) = 2/8 = 1/4 = 0.250.

Question 8

Excel's EXPON.DIST function can be used to compute
A)exponents
B)exponential probabilities
C)cumulative exponential probabilities
D)Both exponential probabilities and cumulative exponential probabilities are correct.

Accepted Answer

The answer of Excel's EXPON.DIST function can be used to...

Question 9

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

Accepted Answer

An exponential probability distribution is a continuous distribution defined by a parameter called the rate parameter. It describes the amount of time between two successive events in a Poisson process. Therefore, it cannot be a discrete distribution. It also doesn't have to be normally distributed.

Question 10

Exhibit 6-4
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 6-4. 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

Accepted Answer

To find the probability that a randomly selected individual with an MBA degree will get a starting salary of at least $30,000, we need to find the area under the normal distribution curve to the right of $30,000.

Using the z-score formula:

z = (x - μ) / σ

where x = $30,000, μ = $40,000, and σ = $5,000

z = (30,000 - 40,000) / 5,000

z = -2

Using a standard normal distribution table or calculator, we can find that the probability of a z-score less than or equal to -2 is 0.0228.

However, we need the probability of a z-score greater than or equal to -2, which is 1 - 0.0228 = 0.9772.

Therefore, the answer is B.

Question 11

Exhibit 6-3
The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds.
-Refer to Exhibit 6-3. What is the minimum weight of the middle 95% of the players?
A)196
B)151
C)249
D)None of the alternative answers is correct.

Accepted Answer

The answer of Exhibit 6-3
The weight of football players is...

Question 12

Exhibit 6-2
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 6-2. 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

Accepted Answer

The probability of finishing the trip in 80 minutes or less is the area under the uniform distribution curve between 40 and 80, which is (80-40)/(90-40) = 0.8.

Question 13

Exhibit 6-1
Consider the continuous random variable x, which has a uniform distribution over the interval from 20 to 28.
-Refer to Exhibit 6-1. The variance of x is approximately
A)2.309
B)5.333
C)32
D)0.667

Accepted Answer

The variance of a continuous uniform distribution is (b-a)^2/12, where a and b are the endpoints of the interval. Therefore, the variance of x is (28-20)^2/12 = 5.333.

Question 14

Excel's EXPON.DIST function has how many inputs?
A)2
B)3
C)4
D)5

Accepted Answer

The EXPON.DIST function in Excel has three inputs - x, lambda (rate), and cumulative (optional).

Question 15

Exhibit 6-3
The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds.
-Refer to Exhibit 6-3. The probability of a player weighing less than 250 pounds is
A)0.4772
B)0.9772
C)0.0528
D)0.5000

Accepted Answer

To find the probability of a player weighing less than 250 pounds, we first need to standardize the value.

z = (250-200)/25
z = 2

Using a standard normal distribution table, we can find the probability of a z-score less than 2 is approximately 0.9772. Therefore, the probability of a football player weighing less than 250 pounds is 0.9772.

Question 16

Exhibit 6-3
The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds.
-Refer to Exhibit 6-3. The probability of a player weighing more than 241.25 pounds is
A)0.4505
B)0.0495
C)0.9505
D)0.9010

Accepted Answer

Using the Z-score formula: 
z = (x - μ) / σ = (241.25 - 200) / 25 = 1.65
Looking up the area to the right of z = 1.65 in the standard normal distribution table or using a calculator, we get the probability of 0.0495 or approximately 4.95%. Therefore, the answer is B.

Question 17

Exhibit 6-2
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 6-2. What is the random variable in this experiment?
A)the uniform distribution
B)40 minutes
C)90 minutes
D)the travel time

Accepted Answer

The random variable in this experiment is the travel time, as it is the outcome being measured and observed. The uniform distribution is the probability distribution for this random variable. 40 and 90 minutes represent the minimum and maximum possible values for the travel time, but they are not the random variable itself.

Question 18

Exhibit 6-4
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 6-4. What is the random variable in this experiment?
A)the starting salaries
B)the normal distribution
C)$40,000
D)$5,000

Accepted Answer

The random variable in this experiment are the starting salaries of individuals with an MBA degree, as they are the values being observed and measured. The normal distribution is not the random variable, but rather the way in which the salaries are distributed. The mean and standard deviation are parameters of the distribution, not the random variable itself.

Question 19

When using Excel's EXPON.DIST function, one should choose TRUE for the third input if
A)a probability is desired
B)a cumulative probability is desired
C)the expected value is desired
D)the correct answer is desired

Accepted Answer

When using the EXPON.DIST function in Excel, the third input determines whether a cumulative probability (TRUE) or a probability density (FALSE) is desired. Therefore, the best choice is B if a cumulative probability is wanted.

Question 20

Exhibit 6-3
The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds.
-Refer to Exhibit 6-3. What is the random variable in this experiment?
A)the weight of football players
B)200 pounds
C)25 pounds
D)the normal distribution

Accepted Answer

The random variable is the weight of football players because it is the variable being measured and is subject to variation (i.e. it can vary from player to player).

Quiz 6: Continuous Probability Distributions

Exhibit 6-1 Consider the continuous random variable x, which has a uniform distribution over the interval from 20 to 28. -Refer to Exhibit 6-1. The probability density function has what value in the interval between 20 and 28?

Exhibit 6-1 Consider the continuous random variable x, which has a uniform distribution over the interval from 20 to 28. -Refer to Exhibit 6-1. The mean of x is

Exhibit 6-2 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 6-2. The probability that her trip will take exactly 50 minutes is

Exhibit 6-1 Consider the continuous random variable x, which has a uniform distribution over the interval from 20 to 28. -Refer to Exhibit 6-1. The probability that x will take on a value between 21 and 25 is

Exhibit 6-2 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 6-2. The probability that her trip will take longer than 60 minutes is

Exhibit 6-3 The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. -Refer to Exhibit 6-3. What percent of players weigh between 180 and 220 pounds?

Exhibit 6-1 Consider the continuous random variable x, which has a uniform distribution over the interval from 20 to 28. -Refer to Exhibit 6-1. The probability that x will take on a value of at least 26 is

Excel's EXPON.DIST function can be used to compute

An exponential probability distribution

Exhibit 6-3 The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. -Refer to Exhibit 6-3. What is the minimum weight of the middle 95% of the players?

Exhibit 6-2 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 6-2. The probability that she will finish her trip in 80 minutes or less is

Exhibit 6-1 Consider the continuous random variable x, which has a uniform distribution over the interval from 20 to 28. -Refer to Exhibit 6-1. The variance of x is approximately

Excel's EXPON.DIST function has how many inputs?

Exhibit 6-3 The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. -Refer to Exhibit 6-3. The probability of a player weighing less than 250 pounds is

Exhibit 6-3 The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. -Refer to Exhibit 6-3. The probability of a player weighing more than 241.25 pounds is

Exhibit 6-2 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 6-2. What is the random variable in this experiment?

Exhibit 6-4 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 6-4. What is the random variable in this experiment?

When using Excel's EXPON.DIST function, one should choose TRUE for the third input if

Exhibit 6-3 The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. -Refer to Exhibit 6-3. What is the random variable in this experiment?