Question 1

Historical data show that the average number of patient arrivals at the intensive care unit of General Hospital is 3 patients every 2 hours. Assume that the patient arrivals are distributed according to a Poisson distribution. Determine the probability of at least 4 but no more than 8 patients arriving in a three-hour period.

Accepted Answer

A)  .3813 
B)  .5711 
C)  .4276 
D)  .7861 
E)  .6174

Question 2

A pharmaceutical company has determined that if a new cholesterol-reducing drug is manufactured and introduced to the market, the following probability distribution will describe the contribution of this drug to their profits during the next six months.  The company management has decided to market this product if the expected contribution to profit for the next six months is more than $1,000,000. Based on the information given above, should the company begin manufacturing the new drug? Explain your answer.

Accepted Answer

A)  Yes, begin manufacturing. 
B)  No, do not begin manufacturing.

Question 3

Depending on the mean of the Poisson distribution, the distribution can either be very skewed to the right or can be quite symmetrical.

Accepted Answer

A) True 
 B)False

Question 4

The probability that a given computer chip will fail is .02. Find the probability that of 5 delivered chips, exactly 2 chips will fail.

Accepted Answer

A)  .9962 
B)  .0999 
C)  .0038 
D)  .0000

Question 5

A discrete variable that can often be used to describe the number of occurrences of an event over a specified interval of time or space is a ________ random variable.

Accepted Answer

A)  Poisson 
B)  discrete 
C)  hypergeometric 
D)  continuous

Question 6

In a binomial distribution, the random variable x is continuous.

Accepted Answer

A) True 
 B)False

Question 7

In the most recent election, 19 percent of all eligible college students voted. If a random sample of 20 students were surveyed, find the probability that none of the students voted.

Accepted Answer

A)  .0000 
B)  .0014 
C)  .0148 
D)  .9852

Question 8

The Post Office has established a record in a major midwestern city for delivering 90 percent of its local mail the next working day. Calculate the standard deviation of the number delivered when 8 local letters are mailed.

Accepted Answer

A)  .85 
B)  .72 
C)  2.68 
D)  2.83

Question 9

A discrete random variable may assume a countable sequence or list.

Accepted Answer

A) True 
 B)False

Question 10

The Post Office has established a record in a major midwestern city for delivering 90 percent of its local mail the next working day. If you mail eight local letters, what is the probability that all of them will be delivered the next day?

Accepted Answer

A)  1.0 
B)  .4305 
C)  .8131 
D)  .5695

Question 11

A correlation coefficient is a unitless measure of the linear relationship between two random variables.

Accepted Answer

A) True 
 B)False

Question 12

The J.O. Supplies Company buys calculators from a non-U.S. supplier. The probability of a defective calculator is 10 percent. If 100 calculators are selected at random, what is the standard deviation of the number of defective calculators?

Accepted Answer

A)  9.00 
B)  3.17 
C)  9.49 
D)  3.00

Question 13

Consider a Poisson distribution with an average of 3 customers per minute at the local grocery store. If X = the number of arrivals per minute, find the variance of X.

Accepted Answer

A)  3 
B)  9 
C)  1.5 
D)  1.7

Question 14

Historical data for a local manufacturing company show that the average number of defects per product produced is 2. In addition, the number of defects per unit is distributed according to a Poisson distribution. A batch has just been completed. What is the probability that the first three units manufactured in this batch will contain at least a total of 4 defects?

Accepted Answer

A)  .8488 
B)  .7149 
C)  .1512 
D)  .2851

Question 15

If x is a Poisson random variable with a mean of 10, what is the probability that x is greater than 6?

Accepted Answer

A)  .9329 
B)  .1301 
C)  .8698 
D)  .0631

Question 16

A manufacturer tested a sample of semiconductor chips and found that 35 were defective and 190 were good. If additional tests are to be conducted with random samples of 160 semiconductor chips, find the mean for the number of defects in these groups of 160 (rounded to the nearest whole number).

Accepted Answer

A)  56 
B)  35 
C)  29 
D)  25

Question 17

Suppose you randomly select 3 DVDs from a production run of 10. Of the 10 DVDs, 9 are expected to last a minimum of 3 years. What values of x are within two standard deviations of the mean?

Accepted Answer

The answer of Suppose you randomly select 3 DVDs from...

Question 18

The Post Office has established a record in a major midwestern city for delivering 90 percent of its local mail the next working day. When there are 8 local letters mailed, what is the probability that the number delivered will be within 2 standard deviations of the mean?

Accepted Answer

A)  .9950 
B)  .9619 
C)  .8131 
D)  .9996

Question 19

A hypergeometric random variable x has a distribution that is approximated by a binomial distribution when

Accepted Answer

A)  the number of successes is larger than the number of failures in the population. 
B)  a sample is selected from the population without replacement. 
C)  the population is much larger (about 20 times larger) than the sample size. 
D)  the sample size is half the size of the original population.

Question 20

If p = .5 and n = 4, then the corresponding binomial distribution is ________.

Accepted Answer

A)  right skewed 
B)  left skewed 
C)  symmetric 
D)  bimodal

Exam 6: Discrete Random Variables

Depending on the mean of the Poisson distribution, the distribution can either be very skewed to the right or can be quite symmetrical.

The probability that a given computer chip will fail is .02. Find the probability that of 5 delivered chips, exactly 2 chips will fail.

A discrete variable that can often be used to describe the number of occurrences of an event over a specified interval of time or space is a ________ random variable.

In a binomial distribution, the random variable x is continuous.

In the most recent election, 19 percent of all eligible college students voted. If a random sample of 20 students were surveyed, find the probability that none of the students voted.

The Post Office has established a record in a major midwestern city for delivering 90 percent of its local mail the next working day. Calculate the standard deviation of the number delivered when 8 local letters are mailed.

A discrete random variable may assume a countable sequence or list.

The Post Office has established a record in a major midwestern city for delivering 90 percent of its local mail the next working day. If you mail eight local letters, what is the probability that all of them will be delivered the next day?

A correlation coefficient is a unitless measure of the linear relationship between two random variables.

The J.O. Supplies Company buys calculators from a non-U.S. supplier. The probability of a defective calculator is 10 percent. If 100 calculators are selected at random, what is the standard deviation of the number of defective calculators?

Consider a Poisson distribution with an average of 3 customers per minute at the local grocery store. If X = the number of arrivals per minute, find the variance of X.

If x is a Poisson random variable with a mean of 10, what is the probability that x is greater than 6?

A manufacturer tested a sample of semiconductor chips and found that 35 were defective and 190 were good. If additional tests are to be conducted with random samples of 160 semiconductor chips, find the mean for the number of defects in these groups of 160 (rounded to the nearest whole number) .

Suppose you randomly select 3 DVDs from a production run of 10. Of the 10 DVDs, 9 are expected to last a minimum of 3 years. What values of x are within two standard deviations of the mean?

The Post Office has established a record in a major midwestern city for delivering 90 percent of its local mail the next working day. When there are 8 local letters mailed, what is the probability that the number delivered will be within 2 standard deviations of the mean?

A hypergeometric random variable x has a distribution that is approximated by a binomial distribution when

If p = .5 and n = 4, then the corresponding binomial distribution is ________.