Question 1

Excel's =100*RAND() function produces continuous random numbers that are uniformly distributed between 0 and 100.The standard deviation of this distribution is approximately:

Accepted Answer

A)   50.00.
B)   28.87.
C)   33.33.
D)   25.00.E) C) and D)
F) A) and D)

Question 2

Regarding continuous probability distributions,which statement is incorrect?

Accepted Answer

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.E) A) and B)
F) C) and D)

Question 3

In a continuous distribution the

Accepted Answer

A)   PDF is usually higher than the CDF.
B)   CDF is used to find left-tail probabilities.
C)   PDF shows the area under the curve.
D)   CDF is usually the same as the PDF.E) A) and B)
F) All of the above

Question 4

A machine dispenses water into a glass.Assuming that the amount of water dispensed follows a continuous uniform distribution from 10 ounces to 16 ounces,the average amount of water dispensed by the machine is:

Accepted Answer

A)   12 ounces.
B)   13 ounces.
C)   14 ounces.
D)   16 ounces.E) B) and C)
F) A) and C)

Question 5

In Melanie's Styling Salon,the time to complete a simple haircut is normally distributed with a mean of 25 minutes and a standard deviation of 4 minutes.For a simple haircut,the middle 90 percent of the customers will require:

Accepted Answer

A)   between 18.4 and 31.6 minutes.
B)   between 19.9 and 30.1 minutes.
C)   between 20.0 and 30.0 minutes.
D)   between 17.2 and 32.8 minutes.E) A) and D)
F) C) and D)

Question 6

A continuous uniform distribution U(0,800)will have μ = 400 and σ = 230.94.

Accepted Answer

A) True 
 B)False

Question 7

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?

Accepted Answer

A)   .8000
B)   .7135
C)   .2865
D)   .5000E) B) and C)
F) A) and D)

Question 8

If the mean waiting time for the next arrival is 12 minutes,what is the median waiting time?

Accepted Answer

A)   7.2 minutes
B)   8.3 minutes
C)   9.1 minutes
D)   12 minutesE) A) and B)
F) All of the above

Question 9

The height and width of a continuous uniform distribution's PDF are the same.

Accepted Answer

A) True 
 B)False

Question 10

A random variable X is best described by a continuous uniform distribution from 20 to 45 inclusive.What is P(30 ≤ X ≤ 40) ?

Accepted Answer

A)   .20
B)   .40
C)   .60
D)   .80E) All of the above
F) A) and B)

Question 11

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?

Accepted Answer

A)   .1393
B)   .8607
C)   .0952
D)   .9048E) A) and B)
F) None of the above

Question 12

The MPG (miles per gallon) for a certain compact car is normally distributed with a mean of 31 and a standard deviation of 0.8.What is the probability that the MPG for a randomly selected compact car would be less than 32?

Accepted Answer

A)   0.3944
B)   0.8944
C)   0.1056
D)   0.5596E) B) and D)
F) B) and C)

Question 13

The probability that a rental car will be stolen is 0.001.If 25,000 cars are rented from Hertz,what is the normal approximation to the probability that fewer than 20 will be stolen?

Accepted Answer

A)   .2577
B)   .1335
C)   .1128
D)   .8335E) A) and B)
F) All of the above

Question 14

The time required for a citizen to complete the 2010 U.S.Census "long" form is normally distributed with a mean of 40 minutes and a standard deviation of 10 minutes.What is the third quartile (in minutes) for the time required to complete the form?

Accepted Answer

A)   44.75
B)   46.75
C)   47.50
D)   52.50E) B) and C)
F) B) and D)

Question 15

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:

Accepted Answer

A)   20,180 hours.
B)   28,782 hours.
C)   23,733 hours.
D)   18,724 hours.E) A) and D)
F) B) and C)

Question 16

The Excel function =40*RAND() would generate random numbers with standard deviation approximately equal to

Accepted Answer

A)   13.33.
B)   20.00.
C)   11.55.
D)   19.27.E) B) and D)
F) C) and D)

Question 17

For a continuous random variable,the total area beneath the PDF will be greater than zero but less than one.

Accepted Answer

A) True 
 B)False

Question 18

The number of lightning strikes in a day in Miami is a continuous random variable.

Accepted Answer

A) True 
 B)False

Question 19

The lengths of brook trout caught in a certain Colorado stream are normally distributed with a mean of 14 inches and a standard deviation of 3 inches.What proportion of brook trout caught will be between 12 and 18 inches in length?

Accepted Answer

A)   .6563
B)   .6826
C)   .2486
D)   .4082E) A) and B)
F) A) and C)

Question 20

The exponential distribution is always skewed right.

Accepted Answer

A) True 
 B)False

Exam 7: Continuous Probability Distributions

For a continuous random variable,the total area beneath the PDF will be greater than zero but less than one.

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Regarding continuous probability distributions,which statement is incorrect?

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The time required for a citizen to complete the 2010 U.S.Census "long" form is normally distributed with a mean of 40 minutes and a standard deviation of 10 minutes.What is the third quartile (in minutes) for the time required to complete the form?

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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:

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If the mean waiting time for the next arrival is 12 minutes,what is the median waiting time?

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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?

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The height and width of a continuous uniform distribution's PDF are the same.

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The exponential distribution is always skewed right.

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The MPG (miles per gallon) for a certain compact car is normally distributed with a mean of 31 and a standard deviation of 0.8.What is the probability that the MPG for a randomly selected compact car would be less than 32?

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In Melanie's Styling Salon,the time to complete a simple haircut is normally distributed with a mean of 25 minutes and a standard deviation of 4 minutes.For a simple haircut,the middle 90 percent of the customers will require:

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Excel's =100*RAND() function produces continuous random numbers that are uniformly distributed between 0 and 100.The standard deviation of this distribution is approximately:

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A continuous uniform distribution U(0,800)will have μ = 400 and σ = 230.94.

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The probability that a rental car will be stolen is 0.001.If 25,000 cars are rented from Hertz,what is the normal approximation to the probability that fewer than 20 will be stolen?

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The Excel function =40*RAND() would generate random numbers with standard deviation approximately equal to

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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?

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The number of lightning strikes in a day in Miami is a continuous random variable.

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In a continuous distribution the

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A random variable X is best described by a continuous uniform distribution from 20 to 45 inclusive.What is P(30 ≤ X ≤ 40) ?

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The lengths of brook trout caught in a certain Colorado stream are normally distributed with a mean of 14 inches and a standard deviation of 3 inches.What proportion of brook trout caught will be between 12 and 18 inches in length?

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A machine dispenses water into a glass.Assuming that the amount of water dispensed follows a continuous uniform distribution from 10 ounces to 16 ounces,the average amount of water dispensed by the machine is:

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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:

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