Answer
a)0.9999
b)0.9641. Money cannot be saved.
Work Step by Step
a) $z_{2}=\frac{value-mean}{standard \ deviation}=\frac{22-18.2}{1}=3.8$
Using the table, the probability of z being less than 3.8: 0.9999.
b) By using the Central Limit Theorem, the sample mean has a mean of $\mu$ and standard deviation of $\frac{\sigma}{\sqrt n}$.
$z=\frac{value-mean}{standard \ deviation}=\frac{18.5-18.2}{\frac{1}{\sqrt{36}}}=1.8.$
Using the table, the probability of z being less than 1.8: 0.9641.
The probability is high, but this doesn't mean that all men would fit in but that most of them would. Hence money cannot be saved.
