Show that, in the notation of (3.4), the expectation of a hypergeometric random variable with parameters  is . Use the CLT to estimate the probability that the number Y of heads appearing in 100...

Show that, in the notation of (3.4), the expectation of a hypergeometric random variable with parameters
 is
.

Use the CLT to estimate the probability that the number Y of heads appearing in 100 tosses of a fair coin

(a) is exactly 50.                                (b) lies between 40 and 60.

(A spreadsheet with a built-in normal cdf function is useful here.) Find the exact probability for part (a).