4.14 Homework  (Page 5/7)

Refer to the previous problem . Suppose that 100 people with tax returns over $25,000 are randomly picked. We are interested in the number of people audited in 1 year. One way to solve this problem is by using the Binomial Distribution. Since $n$ is large and $p$ is small, another discrete distribution could be used to solve the following problems. Solve the following questions (d-f) using that distribution.

• d How many are expected to be audited?
• e Find the probability that no one was audited.
• f Find the probability that more than 2 were audited.

Suppose that a technology task force is being formed to study technology awareness among instructors. Assume that 10 people will be randomly chosen to be on the committee from a group of 28 volunteers, 20 who are technically proficient and 8 who are not. We are interested in the number on the committee who are not technically proficient.

• d How many instructors do you expect on the committee who are not technically proficient?
• e Find the probability that at least 5 on the committee are not technically proficient.
• f Find the probability that at most 3 on the committee are not technically proficient.

Refer back to Exercise 4.15.12 . Solve this problem again, using a different, though still acceptable, distribution.

Suppose that 9 Massachusetts athletes are scheduled to appear at a charity benefit. The 9 are randomly chosen from 8 volunteers from the Boston Celtics and 4 volunteers from the New England Patriots. We are interested in the number of Patriots picked.

• d Is it more likely that there will be 2 Patriots or 3 Patriots picked?

On average, Pierre, an amateur chef, drops 3 pieces of egg shell into every 2 batters of cake he makes. Suppose that you buy one of his cakes.

• d On average, how many pieces of egg shell do you expect to be in the cake?
• e What is the probability that there will not be any pieces of egg shell in the cake?
• f Let’s say that you buy one of Pierre’s cakes each week for 6 weeks. What is the probability that there will not be any egg shell in any of the cakes?
• g Based upon the average given for Pierre, is it possible for there to be 7 pieces of shell in the cake? Why?

It has been estimated that only about 30% of California residents have adequate earthquake supplies. Suppose we are interested in the number of California residents we must survey until we find a resident who does not have adequate earthquake supplies.

• d What is the probability that we must survey just 1 or 2 residents until we find a California resident who does not have adequate earthquake supplies?
• e What is the probability that we must survey at least 3 California residents until we find a California resident who does not have adequate earthquake supplies?
• f How many California residents do you expect to need to survey until you find a California resident who does not have adequate earthquake supplies?
• g How many California residents do you expect to need to survey until you find a California resident who does have adequate earthquake supplies?