Twelve of the top 20 finishers in the 2009 PGA Championship at Hazeltine National Golf Club in Chaska, Minnesota, used a Titleist brand golf ball (GolfBallTest website, November 12, 2009). Suppose these results are representative of the probability that a randomly selected PGA Tour player uses a Titleist brand golf ball. For a sample of 15 PGA Tour players, make the following calculations.

a. Compute the probability that exactly 10 of the 15 PGA Tour players use a Titleist brand golf ball.

b. Compute the probability that more than 10 of the 15 PGA Tour players use a Titleist brand golf ball.

c. For a sample of 15 PGA Tour players, compute the expected number of players who use a Titleist brand golf ball.

d. For a sample of 15 PGA Tour players, compute the variance and standard deviation of the number of players who use a Titleist brand golf ball.