Chapter 6 - The Normal Distribution - 6-3 The Central Limit Theorem - Extending the Concepts - Page 353: 26

0.0025

Given $\mu=72.0,\sigma=5.3,N=500,n=50,X=70$ since $n/N=50/500=0.1>0.05$, we should used the correction factor for the standard error, hence $\sigma_{\bar X}=\frac{5.3}{\sqrt {50}}\times\sqrt {\frac{500-50}{500-1}}=0.7118$ thus $z=\frac{70-72}{0.7119}=-2.8098$ and with table E or a calculator $P(X<70)=P(z)=0.0025$