Problems

1. Suppose that, on average, 4 percent of all CD drives received by a computer company are defective. The company has adopted the following policy: Sample 50 CD drives in each shipment, and accept the shipment if none are defective. Using this information, determine the following:

   • What fraction of shipments will be accepted?

   • If the policy changes so that a shipment is accepted if only one CD drive in the sample is defective, what fraction of shipments will be accepted?

   • What is the probability that a sample size of 50 will contain at least 10 defective CD drives?

2. Using the airline overbooking data:

   • Determine how the probability of overbooking varies as the number of tickets sold varies from 100 through 115. Hint: Use a one-way data table.

   • Show how the probability of overbooking varies as the number of tickets sold varies from 100 through 115, and the probability that a ticket holder shows up varies from 80 percent through 95 percent. Hint: Use a two-way data table.

3. Suppose that during each year, a given mutual fund has a 50 percent chance of beating the Standard & Poor’s 500 Stock Index (S&P Index). In a group of 100 mutual funds, what is the probability that at least 10 funds will beat the S&P Index during at least 8 out of 10 years?

4. Professional basketball player Steve Nash is a 90-percent foul shooter.

   • If he shoots 100 free throws, what is the probability that he will miss more than 15 shots?

   • How good a foul shooter would Steve Nash be if he had only a 5 percent chance of making fewer than 90 free throws out of 100 attempts? Hint: Use Goal Seek.

5. When tested for extra sensory perception (ESP), participants are asked to identify the shape of a card from a 25-card deck. The deck consists of 5 cards of each of five shapes. If a person identifies 12 cards correctly, what would you conclude?

6. Suppose that in a group of 100 people, 20 have the flu and 80 do not. If we randomly select 30 people, what is the chance that at least 10 people have the flu?

7. A student is selling magazines for a school fundraiser. There is a 20 percent chance that a given house will buy a magazine. He needs to sell five magazines. Determine the probability that he will need to visit 5, 6, 7,…, 100 houses to sell five magazines.