how to use central limit theorom to find probaility

Question

Use the Central Limit Theorem to find the indicated probability. The sample size is n, the population proportion is p, and the sample proportion is .
n = 160, p = 0.29; P( > 0.3)

Answer 1

z = (.3-.29)/sqrt(.29(1-.29)/160) = 0.278760874

 

From Excel, P(Z >= z) = 1 - normsdist(z) = 1 - 0.609785829 = 0.390214171

.3 * 160 = 48

If we want, we may make a continuity correction.

z = (48.5/160 - .29)/sqrt(.29(1-.29)/160) = 0.365873648

1-normsdist(z) = 0.357229681

 

 

The exact answer is 1-BINOMDIST(48,160,0.29,TRUE) = 0.353355719

 

The continuity correction helped.