4.1 Homework (modified r. bloom)  (Page 5/6)

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?

• E

  What is the probability that all of the volunteers will be from the Celtics

• F

  Is it more likely that more of the volunteers will be from the Patriots or from the Celtics? How do you know?

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?

Refer to the above problem. Suppose you randomly survey 11 California residents. We are interested in the number who have adequate earthquake supplies.

• D

  What is the probability that at least 8 have adequate earthquake supplies?

• E

  Is it more likely that none or that all of the residents surveyed will have adequate earthquake supplies? Why?

• F

  How many residents do you expect will have adequate earthquake supplies?

Suppose we randomly survey 20 pages. We are interested in the number of pages that advertise footwear. Each page may be picked at most once.

• D

  How many pages do you expect to advertise footwear on them?

• E

  Is it probable that all 20 will advertise footwear on them? Why or why not?

• F

  What is the probability that less than 10 will advertise footwear on them?