Suppose a basketball player, Player A, made 80% of her free throw attempts last season and that she continues to shoot free throws at the same rate. Assume that free throw attempts are independent. Let the random variable X be the number of free throws that player A makes in her next 15 attempts.

Question

a) What is the distribution of X?
b) Find the mean and standard deviation of X.
c) Find the probability that player A makes exactly 10 free throws.
d) Find the probability that player A makes at least 8 free throws.

Answer 1

a) Binomial distribution

b) mean = np = 15 * .80 = ?
sd = √npq = √(15)(.80)(.20) = ?
Note: q = 1 - p
I'll let you finish the calculation.

c) Use a binomial probability table. n = 15, p = .80, x = 10

d) You can approximate a normal distribution by using z-scores.
Formula:
z = (x - mean)/sd
x = 8, mean & sd calculated from b) above.
Use a z-table to determine the probability using the z-score.

I hope this will help get you started.