Faith is a 95% free throw shooter. At practice, each player shoots 20 free throws. Let X = the number of free throws Faith makes out of 20 shots. Calculate the mean of X.

Answer 1

The important thing to notice here is that X, the number of free throws Faith makes out of 20 shots, is a random variable. The second thing to notice is that each instance of Faith shooting a free throw can be considered an independent bernoulli trial, i.e. the outcome is that she either makes it or does not. By repeating these trials, observing their outcomes, and then summing these outcomes, we get a Binomial Distribution.

A binomial distribution has the following probability mass function:

nCx p^k q^{n-k}

Where n is the number of trials observed, x is the number of successes observed, p is the probability of success, and q is the probability of failure. In your case, n = 20, x = X, p = .95, and q = .05.

The only thing you have to realize here, though, is that the mean of a Binomial Random Variable is simply:

np

So, if your intuition told you that the mean should be:

np = .95 * 20 = 19

Then you were correct.