Question: According to the USGA, the diameter of a golf ball shall not be less than 1.680 inches. Periodically they check random samples of balls from different manufacturers. If more than 2 out of a random sample of 10 do not meet this standard, they will be removed from the USGA approved-ball list. One golf ball manufacturer determined that 10% of their balls will be less than 1.680 inches in diameter. If a random sample of 10 balls is selected:

A. What is the probability that exactly 3 do not meet specifications?

B. What is the probability 1 or fewer do not meet specifications?

C. What is the probability that the manufacturer will not be on the USGA approved-ball list?

D. What is the mean and standard deviation for the number of balls less than 1.680 inches?

E. If the proportion of balls less than 1.680 inches is less than 10%, how will the answer to “C” change?