It is estimated that 17% of americans have blue eyes. A random sample of 9 americans is selected. Find the probability that the sample includes exactly 2 people with blue eyes. Find the probability that the sample includes at most 2 people with blue eyes. Find the mean number of blu-eyed people in a sample of 9 americans.

Answer 1

Mean = np = 9 * .17 = 1.53

Use binomial probability formula (or a binomial probability table).

Formula:
P(x) = (nCx)(p^x)[q^(n-x)]

x = 0,1,2
n = 9
p = .17
q = 1 - p = 1 - .17 = .83

For first part: Find P(2) for probability.

For second part: Find P(0) and P(1). Add P(0), P(1), and P(2) for probability.

I'll let you take it from here.