6. Suppose you have a friend on the school basketball team but, unfortunately, he is not a good free throw shooter. Over the course of his career, he has only made 40% of his shots. Otherwise, he is a good player and gets fouled a lot so he shoots 10 free throws a game, on average. In the biggest game of the season, he does very well and makes 6 out of 10 free throw attempts. A. Assuming that each shot is independent, set up the expression you would use to determine the exact probability that your friend actually makes 6 or more free throws in a given game.
B. Using the set of random numbers shown here, explain how you would set up a simulation to determine the probability of making 6 or more free throws out of 10 attempts if your probability of making any one free throw is .4.

98713
19464
57512
49898
84837
52245
38816
62042
76406
89744
51623
65847
53436
08320
45677
46304
71946
17871
88983
25948
21826
94930
96270
97988
37221
07174
51855
00969
24384
98095
41970
19537
18910
17433
36753
41545
01058
47896
75215
35996
04853
00796
78602
54962
42771
39128
96541
47221
39264
05585

C. Suppose you wanted to do a normal approximation to the binomial for this situation. What are the mean and standard deviation of the binomial distribution? Is the normal approximation justified in this situation? Explain why or why not? Would the normal approximation be justified if n = 100?

D. One of your friend's attempts during a game is a "one-and-one." That is, if he makes one free throw, he is given the opportunity to take a second shot. Assuming each shot is independent, is he most likely to make 0, 1, or 2 points on a "one-and-one" opportunity.

E. What is the probability that the first free throw he makes is his fourth attempt?