Question

Suppose that population distribution of the variable ”waist size of adult American males in inches” is µ = 33 and σ = 3 and approximately. What is the probability of encountering a man with a waist size smaller than 28 inches? What is the probability of encountering a group of 5 men with a sample average of less than 32?

Answer 1

Given $\mu =33$ and $\sigma =3$

a) We need to find

$Z=\frac{X-\mu }{\sigma }=\frac{28-33}{3}=\frac{-5}{3}=-1.67$

b)We need to find $P(\overline{x}< 32)$

$\mu _{\overline{x}}=\mu =33$ and $\sigma _{\overline{x}}=\frac{\sigma }{\sqrt{n}} =\frac{3}{\sqrt{5}}=1.34$

$Z=\frac{\overline{x}-\mu _{\overline{x}}}{\sigma _{\overline{x}}}=\frac{32-33}{1.34 }=-0.75$

$P(\overline{x}< 32)=P(Z< -0.75)=0.2280$