## Elementary Statistics (12th Edition)

By using the Central Limit Theorem, the sample mean has a mean of $\mu$ and standard deviation of $\frac{\sigma}{\sqrt n}$. $z=\frac{value-mean}{standard \ deviation}=\frac{195.3-182.9}{\frac{40.8}{\sqrt{16}}}=1.22.$ Using the table, the probability of z being more than 1.22 is equal to 1 minus the probability of z being less than 1.22, which is: 1-0.8888=0.1112. Therefore the elevator seems to be safe, because the probability of it being overloaded is not too close to 0.