The Gallup Poll found that about 15% of American adults jogged regularly. A rand

Question

The Gallup Poll found that about 15% of American adults jogged regularly. A random sample of 100 American adults is obtained. What is the expected number of regular joggers in the sample and what is the variance of this number? Using the normal approximation, find the approximate probability that at least 20 are regular jossers. Using the normal approximation, find the probability that there are no more than 10 regular joggers in the sample. Using the normal approximation, find the probability that there are exactly 15 regular joggers in the sample.

Explanation / Answer

1) E[x] = n * p = 100 * .15 = 15 Var[x] = n * p * (1-p) = 100 * .15 * .85 = 12.75 Stdev[x] = sqrt(Var[x]) = 3.57 2) P(X > 20) --> P(x > 19.5) --> 1 - P(x < 19.5) z(19.5) = (19.5 - 15) / 3.57 = 1.26 --> p = .8962 = area to theleft 1 - .8962 = .1038 3) P(X < 10) --> P(x < 10.5) z(10.5) = (10.5 - 15) / 3.57 = -1.26 --> p = .1038 4) P(X = 15) = P(14.5 p = .4443 P(X = 15) = .5557 - .4443 = .1114

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