Question

A population has a mean of 100 and standards of deviation of 20 suppose a simple random sample of size 100 is selected and is used to estimate u . What is the probability that the sample proportion mean will be within +_ 2 of the population mean?

Answer 1

Sample mean is normally distributed with mean $\mu$ and standard deviation $\frac{\sigma}{\sqrt{n}}$

$P(98<x<102)=P(-0.2<z<0.2)$

From =NORM.S.DIST(0.2,TRUE)-NORM.S.DIST(-0.2,TRUE) Excel formula, the answer is 0.15852