Regarding Discrete Random Variables.

Question 1

United Medicine, Inc., claims that a drug, Viro, significantly relieves the

symptoms of a certain viral infection for 80 percent of all patients. Suppose that

this drug is given to eight randomly selected patients who have been diagnosed

with viral infection.

a Let x equal the number of the eight randomly selected patients whose symptoms

are significantly relieved. What distribution describes the random variable x?

Explain.

b Assuming that the company's claim is correct, find . P(x<3).

c Suppose that of the eight randomly selected patients, three have had their

symptoms significantly relieved by Viro. Based on the probability in part b,

would you believe the claim of United Medicine, Inc.? Explain.

Question 2

A consumer advocate claims that 80 percent of cable television subscribers

are not satisfied with their cable service. In an attempt to justify this claim, a

randomly selected sample of cable subscribers will be polled on this issue.

a. Suppose that the advocate's claim is true, and suppose that a random sample of

five cable subscribers is selected. Assuming independence, use an appropriate

formula to compute the probability that four or more subscribers in the sample

are not satisfied with their service.

b. Suppose that the advocate's claim is true, and suppose that a random sample of

25 cable subscribers is selected. Assuming independence, use a computer to

find

(1) The probability that 15 or fewer subscribers in the sample are not

satisfied with their service.

(2) The probability that more than 20 subscribers in the sample are not

satisfied with their service.

(3) The probability that between 20 and 24 (inclusive) subscribers in the

sample are not satisfied with their service.

(4) The probability that exactly 24 subscribers in the sample are not

satisfied with their service.

c. Suppose that when we survey 25 randomly selected cable television subscribers, we find that 15 are actually not satisfied with their service. Using a

probability you found in this exercise as the basis for your answer, do you

believe the consumer advocate's claim? Explain.

Question 3

A retail store has implemented procedures aimed at reducing the number of

bad checks cashed by its cashiers. The store's goal is to cash no more than eight

bad checks per week. The average number of bad checks cashed is three per week.

Let x denote the number of bad checks cashed per week. Assuming that x has a

Poisson distribution:

a Find the probability that the store's cashiers will not cash any bad checks in a

particular week.

b Find the probability that the store will meet its goal during a particular week.

c Find the probability that the store will not meet its goal during a particular

week.

d Find the probability that the store's cashiers will cash no more than 10 bad

checks per two-week period.

e Find the probability that the store's cashiers will cash no more than five bad

checks per three-week period.