Minitab 7. the census bureau's current population survey shows 28% of individuals, ages 25 and older, have completed four years of college. for a sample of 15 individuals, ages 25 and older, what is the probability that three or more will have completed four years of college?

We use the binomial probability equation:

P = nCr * p^r * q^ (n-r)

where n is number of samples = 15, r number who completed = 3 or more, p = 0.28, q = 1-0.28 = 0.72

In this case, we will solve for P when r = 0, 1 and 2 then deduct it from P = 1.

when r = 0, P = 15C0 * 0.28^0 * 0.72^ (15-0) = 7.244x10^-3

when r = 1, P = 15C1 * 0.28^1 * 0.72^ (15-1) = 0.04226

when r = 2, P = 15C2 * 0.28^2 * 0.72^ (15-2) = 0.115

P (r = 0 to r = 2) = 0.1645

So,

P (r = 3 to 15) = 1 - 0.1645 = 0.8355 = 83.55%