Question 1

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 2

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 exponential distribution is appropriate for modeling the waiting time until a specific event occurs, such as the breakdown of a photocopier. The exponential distribution describes the time between events in a Poisson process, where the events occur randomly and independently over time. The Poisson distribution could also be used in this case, but it would describe the number of breakdowns over a certain time period rather than the waiting time until a specific event occurs. The normal and uniform distributions are not appropriate in this case since they do not account for the randomness and independence of the events.

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) .1393
B) .8607
C) .0952
D) .9048

Accepted Answer

The average time between major earthquakes in the California county is approximately 3 years (since there are 10-year spans between earthquakes on average). Therefore, the average probability of an earthquake occurring in any given six-month span is 0.25 (0.5/3). 
The probability of less than six months passing without an earthquake is the same as the probability of an earthquake occurring in the next six-month span, which is 0.25. 
Therefore, the answer is A: .1393.

Question 4

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, the variable can take any value between negative infinity and positive infinity.

Question 5

Bob's z-score for the last exam was -1.15 in FIN 417,"Capital Budgeting Strategies." 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

According to normal distribution, the bottom quartile covers the lowest 25% of scores. A z-score of -1.15 indicates that Bob's score is 1.15 standard deviations below the mean. Using a standard normal distribution table, we can see that the proportion of scores falling below a z-score of -1.15 is approximately 0.1251, which is less than 0.25. Therefore, Bob's score is indeed within the bottom quartile.

Question 6

If the mean time between in-flight aircraft engine shutdowns is 12,500 operating hours,the 90^th 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

To find the waiting time for a specific percentile, we need to use the exponential distribution formula: 
P(X > x) = e^(-λx)
where λ = 1/12500 (the rate parameter)
and P(X > x) = 0.901 (the desired percentile)

So, 
0.901 = e^(-λx) 
ln(0.901) = -λx 
x = ln(0.901)/(-λ) 
x = ln(0.901)/(-1/12500) 
x ≈ 28,782 hours

Therefore, the 90th percentile of waiting times to the next shutdown is approximately 28,782 hours.

Question 7

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 8

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) 68^th B) 75^th C) 84^th D) 92^nd

Accepted Answer

The answer of Exam scores were normal in MIS 200.Jason's...

Question 9

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) .1353
B) .6044
C) .7389
D) .8647

Accepted Answer

The time between discoveries of fraudulent corporate tax returns follows an exponential distribution with a mean of 15 minutes. The probability that less than 30 minutes will elapse is given by 1 - e^(-30/15) = 1 - e^(-2) ≈ 0.8647.

Question 10

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

Accepted Answer

We need to find the value of X such that P(X ≤ x) = 0.6710.

Using the standard normal distribution table, we can find that the z-score corresponding to the 0.6710 percentile is approximately 0.44.

We can convert this z-score back to the original scale using the formula:

z = (X - μ) / σ

0.44 = (X - 80) / 6

X = 83.64

Therefore, the 67th percentile of the normal distribution with mean 80 and variance 36 is approximately 83.64.

Rounding it off to two decimal places, we get:

83.64 ≈ 82.64

Thus the answer is D, 82.64.

Question 11

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, which is represented by the letter "σ". Therefore, the correct choice is D, with μ = 0 and σ = 1.

Question 12

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) .8000
B) .7135
C) .2865
D) .5000

Accepted Answer

We can use the exponential distribution formula with mean of 4,000 hours and x = 5,000 hours to find the probability of unscheduled maintenance in the next 5,000 hours:
P(x < 5,000) = 1 - e^(-5,000/4,000) = 0.7135. Therefore, the answer is B.

Question 13

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 divide the result by the standard deviation. This transformation standardizes X into a Z-score representing the number of standard deviations away from the mean.

Question 14

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

Accepted Answer

The normal distribution is symmetric and not skewed, meaning its skewness is zero. This makes statement C incorrect as it suggests the normal distribution can sometimes be skewed.

Question 15

The area under the normal curve between the 20^th and 70^th percentiles is equal to: A) 0.7000. B) 0.5000. C) 0.9193. Logically,this must be .70 - .20 = .50,as you can verify from Appendix C

Accepted Answer

The area between the 20th and 70th percentiles of a normal curve is exactly 50% (0.5). This can be verified using Appendix C or by understanding that the normal curve is symmetrical and the area under the curve between the 0th and 50th percentiles is also 50%. Thus, the answer is B) 0.5000.

Question 16

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) Triangular
B) Uniform
C) Normal
D) Exponential

Accepted Answer

The waiting time until getting the next nonworking web URL for Florida condo rentals is best described by the exponential distribution, as it is a continuous random variable with a constant failure rate, meaning that the probability of experiencing a nonworking URL at any given time is constant. The other distributions (triangular, uniform, and normal) are not appropriate for this situation.

Question 17

If GMAT scores for applicants at Oxnard Graduate School of Business are N(500,50)then the top 5 percent of the applicants would have a score of at least (choose the nearest integer):
A) 575.
B) 582.
C) 601.
D) 608

Accepted Answer

To find the score that corresponds to the top 5% of applicants, we need to find the z-score that corresponds to the 95th percentile, which is approximately 1.645 (found using a standard normal distribution table or calculator).

We can then use the formula: 
z = (x - μ)/σ
where z is the z-score, x is the score we want to find, μ is the mean (500), and σ is the standard deviation (50).

Substituting the values, we get: 
1.645 = (x - 500) / 50

Solving for x: 
x = 1.645 * 50 + 500 = 582.25

Rounding to the nearest integer gives us a score of 582, which is closest to choice B.

Question 18

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) .8187
B) .0488
C) .1813
D) .2224

Accepted Answer

This problem involves the exponential distribution with a rate parameter of λ = 1/30, since breakdowns are occurring continuously over time. The probability that less than 6 minutes will elapse before the next breakdown can be found by calculating the cumulative distribution function (CDF) of the exponential distribution evaluated at t = 6.

F(6) = 1 - e^(-λt) = 1 - e^(-1/30 * 6) = 0.1813

Therefore, the probability that less than 6 minutes will elapse before the next breakdown is 0.1813, or approximately 18.13%. The answer is C.

Question 19

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 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 can have different means and standard deviations but they both have the same shape, which is determined by the normal distribution formula. Skewness and kurtosis, on the other hand, are measures of the shape of a distribution and can vary between different types of distributions.

Quiz 7: Continuous Probability Distributions

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) ?

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?

The variable in a normal distribution can assume any value between

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

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

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:

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

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?

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

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

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?

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

Regarding continuous probability distributions,which statement is incorrect?

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

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?

If GMAT scores for applicants at Oxnard Graduate School of Business are N(500,50) then the top 5 percent of the applicants would have a score of at least (choose the nearest integer) :

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

Any two normal curves are the same except for their: