## Elementary Statistics (12th Edition)

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.