Help with central limit theorem in statistics?

Question

Among the adults in a large city, 30% have a college degree. A simple random sample of 100 adults is chosen. What is the probability that more than 35 of them have a college degree?

BeeFree · Accepted Answer

CrazyAzn89 -

This is Binomial with n=100 and p = 0.3.  However, you can approximate the Binomial with the Standard Normal if n is large. Under this case,

mean = np = 100(.3) = 30
std. dev. = sqrt (npq) = 4.583

Adjusting for Continuity:

P(X > 35.5) = P[(z > (35.5 - 30)/4.583] = P(z > 1.2),  looking this up in a Standard Normal:

P(z > 1.2) = P(z < -1.2) = 0.115

Hope that helps

P.S. if you used Binomial the exact answer is 0.116

Help with central limit theorem in statistics?

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