Question: A new weight reduction program is to be tested on N overweight people. They were each weighed before starting the program. After one month, they were weighed again. It was observed that k of these lost weight. Now, weight does not remain constant, and one might assume that if the program did not work, a person’s weight is equally likely to go up as go down during the month.

(a) Assuming that the program had no effect whatsoever, what is the probability that at least k of these people lost weight?

(b) If \(\beta \) is the largest of the unbelievably small probabilities, what conclusion will you draw?