Question

The mean cholesterol level for US adults was 199, with a standard deviation of 39. A simple random sample of 107 adults is chosen. Use the Cumulative Normal Distribution Table . Round to four decimals.

A) What is the probability that the mean cholesterol level is greater than 207?

B) What is the probability that the sample mean cholesterol level is between 187 and 193?

Answer 1

A) $Z=\frac{x-\overline{x}}{\frac{\sigma}{\sqrt{n}} }=\frac{207-199}{\frac{39}{\sqrt{107 }}}=\frac{8}{3.77}=2.12$

$P(\overline{x}> 207)=P(Z>2.12 )=0.0170$

B)$Z_{1}=\frac{x_{1}-\overline{x}}{\frac{\sigma}{\sqrt{n}} }=\frac{187-199}{\frac{39}{\sqrt{107 }}}=\frac{-12}{3.77}=-3.18$

$Z_{2}=\frac{x_{2}-\overline{x}}{\frac{\sigma}{\sqrt{n}} }=\frac{193-199}{\frac{39}{\sqrt{107 }}}=\frac{-6}{3.77}=-1.59$

$P(187< \overline{x}< 193)=P(-3.18< Z< -1.59 )=0.0562$