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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.
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.

  • Statistics -

    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.
    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.

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