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 5.23

5.23 Random stock prices.

As noted in Example 5.4(a) (page 246), the S&P 500 index has a probability 0.56 of increasing in any week. Moreover, the change in the index in any given week is not influenced by whether it rose or fell in earlier weeks. Let be the number of weeks among the next five weeks in which the index rises.

  1. has a binomial distribution. What are and ?
  2. What are the possible values that can take?
  3. Use the binomial formula to find the probability of each value of . Draw a probability histogram for the distribution of .
  4. What are the mean and standard deviation of this distribution?

5.23

(a) . (b) . (c) . . . . . . (d) . .