Question 1

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 2

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) .9048

Question 3

The normal distribution is a good approximation to the binomial if both π ≥ 10 and n ≥ 10.

Accepted Answer

A) True 
 B)False

Question 4

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.

Question 5

A large number of applicants for admission to graduate study in business are given an aptitude test. Scores are normally distributed with a mean of 460 and standard deviation of 80. What fraction of the applicants would you expect to have a score of 400 or above?

Accepted Answer

A) 0.2734 
B) 0.7734 
C) 0.7266 
D) 0.7500

Question 6

Compared to the area between z = 1.00 and z = 1.25, the area between z = 2.00 and z = 2.25 in the standard normal distribution will be:

Accepted Answer

A) smaller. 
B) larger. 
C) the same. 
D) impossible to compare without knowing μ and σ.

Question 7

A random variable X is best described by a continuous uniform distribution from 20 to 45 inclusive. The standard deviation of this distribution is approximately:

Accepted Answer

A) 52.1. 
B) 32.5. 
C) 6.85. 
D) 7.22.

Question 8

A continuous uniform distribution U(100, 200) will have the same standard deviation as a continuous uniform distribution U(200,300).

Accepted Answer

A) True 
 B)False

Question 9

In a T-F exam with 100 questions, passing requires a score of at least 60. What is the approximate normal probability that a "guesser" will score at least 60 points?

Accepted Answer

A) .0287 
B) .4713 
C) .0251 
D) .0377

Question 10

The normal is a good approximation to the binomial when n is greater than or equal to 10.

Accepted Answer

A) True 
 B)False

Question 11

A large number of applicants for admission to graduate study in business are given an aptitude test. Scores are normally distributed with a mean of 460 and standard deviation of 80. What fraction of applicants would you expect to have scores of 600 or above?

Accepted Answer

A) 0.0401 
B) 0.4599 
C) 0.5401 
D) 0.0852

Question 12

A student's grade on an examination was transformed to a z value of 0.67. Assuming a normal distribution, we know that she scored approximately in the top:

Accepted Answer

A) 15 percent. 
B) 50 percent. 
C) 40 percent. 
D) 25 percent.

Question 13

The figure shows a normal N(400, 23) distribution. Find the approximate shaded area.  C.2 gives 1 - P(z < 1.74) = 1 - .9591 = .0409, or from Excel =1-NORM.DIST(440,400,23,1) = .0410.

Accepted Answer

A) .0410 
B) .0501 
C) .0724 
D) .0838

Question 14

A multiple choice exam has 100 questions. Each question has five choices. What would be the approximate probability that a "guesser" could achieve a score of 30 or more?

Accepted Answer

A) 0.0088 
B) 0.0062 
C) 0.0015 
D) 0.4913

Question 15

The normal distribution is a good approximation to the binomial if n = 200 and π = .03.

Accepted Answer

A) True 
 B)False

Question 16

The area under an exponential curve can exceed 1 because the distribution is right-skewed.

Accepted Answer

A) True 
 B)False

Question 17

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

Accepted Answer

A) True 
 B)False

Question 18

The area under a normal curve is 1 only if the distribution is standardized N(0, 1).

Accepted Answer

A) True 
 B)False

Question 19

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

Accepted Answer

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.

Question 20

Excel's =RAND() function produces random numbers that are uniformly distributed from 0 to 1. What is the probability that the random number exceeds .75?

Accepted Answer

A) 75 percent 
B) 50 percent 
C) 25 percent

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.

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 normal distribution is a good approximation to the binomial if both π ≥ 10 and n ≥ 10.

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

A large number of applicants for admission to graduate study in business are given an aptitude test. Scores are normally distributed with a mean of 460 and standard deviation of 80. What fraction of the applicants would you expect to have a score of 400 or above?

Compared to the area between z = 1.00 and z = 1.25, the area between z = 2.00 and z = 2.25 in the standard normal distribution will be:

A random variable X is best described by a continuous uniform distribution from 20 to 45 inclusive. The standard deviation of this distribution is approximately:

A continuous uniform distribution U(100, 200) will have the same standard deviation as a continuous uniform distribution U(200,300).

In a T-F exam with 100 questions, passing requires a score of at least 60. What is the approximate normal probability that a "guesser" will score at least 60 points?

The normal is a good approximation to the binomial when n is greater than or equal to 10.

A large number of applicants for admission to graduate study in business are given an aptitude test. Scores are normally distributed with a mean of 460 and standard deviation of 80. What fraction of applicants would you expect to have scores of 600 or above?

A student's grade on an examination was transformed to a z value of 0.67. Assuming a normal distribution, we know that she scored approximately in the top:

The figure shows a normal N(400, 23) distribution. Find the approximate shaded area. C.2 gives 1 - P(z < 1.74) = 1 - .9591 = .0409, or from Excel =1-NORM.DIST(440,400,23,1) = .0410.

A multiple choice exam has 100 questions. Each question has five choices. What would be the approximate probability that a "guesser" could achieve a score of 30 or more?

The normal distribution is a good approximation to the binomial if n = 200 and π = .03.

The area under an exponential curve can exceed 1 because the distribution is right-skewed.

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

The area under a normal curve is 1 only if the distribution is standardized N(0, 1).

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

Excel's =RAND() function produces random numbers that are uniformly distributed from 0 to 1. What is the probability that the random number exceeds .75?