On average, your instructor made just 55% of his free throws in high school.

a. what's the probability he makes four out of five?

Assuming constant probability of p=0.55, we can use the binomial distribution, with n=5, x=4 and p=0.55,

P (X=x) = C (n, x) * p^4 * (1-p) ^ (n-x)

=>

P (X=4) = C (5,4) (0.55) ^4 (0.45) ^1

=5! / (4!1!) (0.55^4) (0.45^1)

=0.2059 (approx.)