## Elementary Statistics (12th Edition)

By using the Central Limit Theorem, the sample mean has a mean of $\mu$ and standard deviation of $\frac{\sigma}{\sqrt n}$. $z=\frac{value-mean}{standard \ deviation}=\frac{167.6-182.9}{\frac{40.8}{\sqrt{16}}}=-2.28.$ Using the table, the probability of z being more than -2.28 is equal to 1 minus the probability of z being less than -2.28, which is: 1-0.0113=0.9887. Therefore the pilot should take over the aeroplane because the probability of it being overloaded is very high.