Most binomial probability calculations required in these exercises can be done by using Table C or the Normal approximation. Your instructor may request that you use the binomial probability formula or software. In exercises requiring the Normal approximation, you should use the continuity correction if you studied that topic.

Question 5.21

5.21 Should you use the binomial distribution?

In each of the following situations, is it reasonable to use a binomial distribution for the random variable ? Give reasons for your answer in each case. If a binomial distribution applies, give the values of and .

  1. A poll of 200 college students asks whether or not they usually feel irritable in the morning. is the number who reply that they do usually feel irritable in the morning.
  2. You toss a fair coin until a head appears. is the count of the number of tosses that you make.
  3. Most calls made at random by sample surveys don’t succeed in talking with a person. Of calls to New York City, only one-twelfth succeed. A survey calls 500 randomly selected numbers in New York City. is the number of times that a person is reached.
  4. You deal 10 cards from a shuffled deck of standard playing cards and count the number of black cards.

5.21

(a) , where is the probability that a student says he or she usually feels irritable in the morning. (b) This is not binomial; there is not a fixed . (c) . (d) This is not binomial because separate cards are not independent.