Question 1

The standard deviation of a normal random variable X is $20.Given that P(X ≤ $10)= 0.1841 we can determine that the mean of the distribution is equal to
A)$13
B)$26
C)$20
D)$28

Accepted Answer

The probability P(X ≤ $10) = 0.1841 corresponds to a z-score of approximately -0.9. Using the z-score formula, z = (X - μ) / σ, where X = 10, σ = 20, and z = -0.9, we can solve for μ: -0.9 = (10 - μ) / 20, which gives μ = 28.

Question 2

A certain assembly line at Vexing Manufacturing Company averages 30 minutes between breakdowns.The median time between breakdowns is
A)30.0 minutes.
B)35.7 minutes.
C)25.4 minutes.
D)20.8 minutes.

Accepted Answer

The answer of A certain assembly line at Vexing Manufacturing...

Question 3

On average,a major earthquake (Richter scale 6.0 or above)occurs 3 times a decade in a certain California county.What is the probability that less than six months will pass before the next earthquake?
A)0.1393
B)0.8607
C)0.0952
D)0.9048

Accepted Answer

The probability that less than six months will pass before the next earthquake is the same as the probability that the next earthquake will occur within the next six months. Since there are 3 earthquakes per decade, the probability of an earthquake occurring in any given six-month period is 3/10 * 1/2 = 3/20 = 0.15. Therefore, the probability that less than six months will pass before the next earthquake is 1 - 0.15 = 0.85.

Question 4

Regarding continuous probability distributions,which statement is correct?
A)The exponential distribution may be skewed left or right.
B)The uniform distribution is never skewed.
C)The normal distribution is sometimes skewed.
D)The standard normal distribution is platykurtic.

Accepted Answer

The uniform distribution is always symmetrical and never skewed.

Question 5

On the last exam in FIN 417,"Capital Budgeting Strategies" Bob's z-score was −1.15.Bob said,"Yipe! My score is within the bottom quartile." Assuming a normal distribution,is Bob right?
A)Yes
B)No
C)Must know the class size to answer

Accepted Answer

A z-score of -1.15 means Bob's score is 1.15 standard deviations below the mean. In a normal distribution, approximately 25% of the data falls below one standard deviation below the mean, so Bob's score would indeed fall within the bottom quartile. Therefore, Bob is correct in his statement.

Question 6

Compared to the area between z = 0.50 and z = 0.75,the area between z = 1.50 and z = 1.75 in the standard normal distribution will be
A)smaller
B)larger
C)the same

Accepted Answer

The area between z = 1.50 and z = 1.75 is smaller because, in a standard normal distribution, as you move further away from the mean (z = 0), the density decreases, meaning there is less area under the curve.

Question 7

Which probability model is most appropriate to describe the waiting time (working days)until an office photocopier breaks down (i.e. ,requires unscheduled maintenance)?
A)Normal
B)Uniform
C)Exponential
D)Poisson

Accepted Answer

The most appropriate probability model for describing the waiting time until a photocopier breaks down is the exponential distribution, as this distribution is often used to model the time until an event occurs (in this case, the breakdown of the photocopier). The exponential distribution is also characterized by the memoryless property, which means that the probability of failure in any future period is not influenced by the length of time already waited.

Question 8

The variable in a normal distribution can assume any value between
A)−3 and +3
B)−4 and +4
C)−1 and +1
D)−∞ and +∞

Accepted Answer

In a normal distribution, there is no limit to the values that the variable can take. It can range from negative infinity to positive infinity. Therefore, D is the best choice.

Question 9

If the mean time between in-flight aircraft engine shutdowns is 12,500 operating hours,the 90th percentile of waiting times to the next shutdown will be
A)20,180 hours.
B)28,782 hours.
C)23,733 hours.
D)18,724 hours.

Accepted Answer

The answer of If the mean time between in-flight aircraft...

Question 10

Exam scores were normal in MIS 200.Jason's exam score was 1.41 standard deviations above the mean.What percentile is he in?
A)68th
B)75th
C)84th
D)92nd

Accepted Answer

Assuming a normal distribution, being 1.41 standard deviations above the mean puts Jason in the 92nd percentile. This means he scored higher than 92% of the class.

Question 11

The area under the normal curve between the 20th and 70th percentiles is equal to
A)0.7000
B)0.5000
C)0.9193

Accepted Answer

The area under the normal curve between the 20th and 70th percentiles represents the middle 50% of the distribution, which corresponds to an area of 0.5000.

Question 12

To convert a normally distributed variable X into a standard Z score we would
A)subtract the mean from the original observation and divide the result by the variance.
B)subtract the mean from the original observation and divide the result by the standard deviation.
C)add the mean and the original observation,then divide by the variance.
D)subtract the mean from the standard deviation and divide by the variance.

Accepted Answer

To convert a normally distributed variable X into a standard Z score, we need to subtract the mean from the original observation and then divide the result by the standard deviation. This gives us a Z score, which is a measure of how many standard deviations the original observation is away from the mean.

Question 13

On average,15 minutes elapse between discoveries of fraudulent corporate tax returns in a certain IRS office.What is the probability that less than 30 minutes will elapse before the next fraudulent corporate tax return is discovered?
A)0.1353
B)0.6044
C)0.7389
D)0.8647

Accepted Answer

The situation can be modeled using an exponential distribution with a mean (λ) of 15 minutes. The probability that less than 30 minutes will elapse is given by the cumulative distribution function (CDF) of the exponential distribution: P(X < 30) = 1 - e^(-30/15) = 1 - e^(-2) ≈ 0.8647.

Question 14

What are the mean and standard deviation for the standard normal distribution?
A)μ = 0,σ = 0
B)μ = 1,σ = 1
C)μ = 1,σ = 0
D)μ = 0,σ = 1

Accepted Answer

The standard normal distribution has a mean of 0 and a standard deviation of 1, so the correct choice is D.

Question 15

A certain assembly line at Vexing Manufacturing Company averages 30 minutes between breakdowns.What is the probability that less than 6 minutes will elapse before the next breakdown?
A)0.8187
B)0.0488
C)0.1813
D)0.2224

Accepted Answer

The time between breakdowns follows an exponential distribution with a mean of 30 minutes. The probability that less than 6 minutes will elapse is found using the cumulative distribution function (CDF) of the exponential distribution: P(X < 6) = 1 - e^(-6/30) = 0.1813.

Question 16

If the mean time between unscheduled maintenance of LCD displays in a hospital's CT scan facility is 4,000 operating hours,what is the probability of unscheduled maintenance in the next 5,000 hours?
A)0.8000
B)0.7135
C)0.2865
D)0.5000

Accepted Answer

The mean time between unscheduled maintenance is 4,000 operating hours, which means the failure rate is (1/4000) per hour. To find the probability of unscheduled maintenance in the next 5,000 hours, we need to use the exponential distribution with the parameter lambda = 1/4000.

P(X < 5000) = 1 - e^(-lambda*X)
P(X < 5000) = 1 - e^(-1/4000 * 5000)
P(X < 5000) = 1 - e^(-1.25)
P(X < 5000) = 0.7135

Therefore, the probability of unscheduled maintenance in the next 5,000 hours is 0.7135, which corresponds to choice B.

Question 17

Which model best describes your waiting time until you get the next nonworking web URL ("This page cannot be displayed")as you click on various websites for Florida condo rentals?
A)Standard normal
B)Uniform
C)Normal
D)Exponential

Accepted Answer

The exponential model is the best choice for describing waiting time until the next nonworking web URL, as it is commonly used to describe the time between successive events that occur independently of each other, such as the failure of web pages to load. The other models listed (Standard normal, Uniform, and Normal) are not appropriate for this scenario.

Question 18

The random variable X is normally distributed with mean of 80 and variance of 36.The 67th percentile of the distribution is
A)72.00
B)95.84
C)90.00
D)82.64

Accepted Answer

We know that the mean (μ) of the normal distribution is 80 and the variance (σ^2) is 36.
Hence, the standard deviation (σ) is the square root of variance i.e. σ = sqrt(36) = 6.

Now, to find the 67th percentile of the distribution, we need to find the z-score corresponding to it.

Using the standard normal distribution table, we can find that the z-score corresponding to the 67th percentile is approximately 0.44.

Therefore,

z = (X - μ) / σ
0.44 = (X - 80)/6
X = 80 + 0.44*6
X = 82.64 (rounded to two decimal places)

Hence, the 67th percentile of the distribution is 82.64.

Therefore, the best choice is (D).

Question 19

Light bulbs are normally distributed with an average lifetime of 1000 hours and a standard deviation of 250 hours.The probability that a light bulb picked at random will last less than 1500 hours is about
A)97.72 percent.
B)95.44 percent.
C)75.00 percent.
D)68.00 percent.

Accepted Answer

To find the probability that a light bulb will last less than 1500 hours, we use the Z-score formula: Z = (X - μ) / σ, where X is the value (1500 hours), μ is the mean (1000 hours), and σ is the standard deviation (250 hours). Plugging in the values, we get Z = (1500 - 1000) / 250 = 500 / 250 = 2. A Z-score of 2 corresponds to approximately 97.72% of the distribution lying below this value, according to the standard normal distribution table.

Question 20

Any two normal curves are the same except for their
A)standard deviations.
B)means.
C)standard deviations and means.
D)standard deviations,means,skewness,and kurtosis.

Accepted Answer

Two normal curves will always have the same shape, which is characterized by the bell curve. The only differences will be in the mean (which shifts the curve left or right) and the standard deviation (which determines how spread out the curve is). Therefore, the correct choice is C, as this option includes both the mean and standard deviation as the only distinguishing factors between the two normal curves. Skewness and kurtosis are not characteristics of normal distributions, as they are typically associated with distributions that are not symmetrical.

Quiz 7: Continuous Probability Distributions

The standard deviation of a normal random variable X is $20.Given that P(X ≤ $10) = 0.1841 we can determine that the mean of the distribution is equal to

A certain assembly line at Vexing Manufacturing Company averages 30 minutes between breakdowns.The median time between breakdowns is

On average,a major earthquake (Richter scale 6.0 or above) occurs 3 times a decade in a certain California county.What is the probability that less than six months will pass before the next earthquake?

Regarding continuous probability distributions,which statement is correct?

On the last exam in FIN 417,"Capital Budgeting Strategies" Bob's z-score was −1.15.Bob said,"Yipe! My score is within the bottom quartile." Assuming a normal distribution,is Bob right?

Compared to the area between z = 0.50 and z = 0.75,the area between z = 1.50 and z = 1.75 in the standard normal distribution will be

Which probability model is most appropriate to describe the waiting time (working days) until an office photocopier breaks down (i.e. ,requires unscheduled maintenance) ?

The variable in a normal distribution can assume any value between

If the mean time between in-flight aircraft engine shutdowns is 12,500 operating hours,the 90th percentile of waiting times to the next shutdown will be

Exam scores were normal in MIS 200.Jason's exam score was 1.41 standard deviations above the mean.What percentile is he in?

The area under the normal curve between the 20th and 70th percentiles is equal to

To convert a normally distributed variable X into a standard Z score we would

On average,15 minutes elapse between discoveries of fraudulent corporate tax returns in a certain IRS office.What is the probability that less than 30 minutes will elapse before the next fraudulent corporate tax return is discovered?

What are the mean and standard deviation for the standard normal distribution?

A certain assembly line at Vexing Manufacturing Company averages 30 minutes between breakdowns.What is the probability that less than 6 minutes will elapse before the next breakdown?

If the mean time between unscheduled maintenance of LCD displays in a hospital's CT scan facility is 4,000 operating hours,what is the probability of unscheduled maintenance in the next 5,000 hours?

Which model best describes your waiting time until you get the next nonworking web URL ("This page cannot be displayed") as you click on various websites for Florida condo rentals?

The random variable X is normally distributed with mean of 80 and variance of 36.The 67th percentile of the distribution is

Light bulbs are normally distributed with an average lifetime of 1000 hours and a standard deviation of 250 hours.The probability that a light bulb picked at random will last less than 1500 hours is about

Any two normal curves are the same except for their