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27 July, 14:17

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?

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  1. 27 July, 14:24
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    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%
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