Question

Marcus Reed hits about 90% of all his free throws. You randomly select 15 of his free throws. Let the random variable X represent the number of free throws Marcus Reed hits out of the 15 selected. Find the mean, variance, and standard deviation of X.

Answer 1

This is a question of Binomial random variable. From the information given;

p = 90% = 0.9
n = sample size = 15

Then, the following calculations can be done:

Mean of X = np = 15*0.9 = 13.5 ≈ 14 throws

Variance of X = np(1-p) = 15*0.9(1-0.9) = 1.35 ≈ 2 throws

Standard deviation of X = Sqrt (variance) = Sqrt (1.35) = 1.16 ≈ 2 throws.