Refer to Example 12 of motors for miniaturized capsules, but instead suppose that 20 motors are available and that 4 will not operate satisfactorily, when placed in a capsule. If the scientist wishes to fabricate two capsules, with two motors each, find the probability that among the four randomly selected motors

(a) all four operate satisfactorily;

(b) three operate satisfactorily and one does not.

Data From Example 12

Transcribed Image Text:

EXAMPLE 12 Using = np to find the mean number of heads in three tosses Find the mean of the probability distribution of the number of heads obtained in 3 flips of a balanced coin. 1 1 3 Solution For a binomial distribution with n = 3 and P = agrees with the result obtained on page 109. we get = 3 = 2 2 and this 2 The formula = np applies, of course, only to binomial distributions. For other special distributions, we can express the mean in terms of their parameters. For instance, for the mean of the hypergeometric distribution with the parameters n, a, and N, we can write