Question

Suppose human weights are normally distributed with mean 175 and standard deviation 36 pounds. A helicopter is evacuating people from a building surrounded by zombies, and this helicopter can fit 9 people and with a maximum weight of 1800 pounds, i.e., an average of 200 pounds per person. If 9 people are randomly chosen to be loaded on this helicopter, what is the probability that it can safely lift off (i.e., the average weight of a person in the helicopter is less than 200)? Keep answers in decimal form and round to THREE decimal places.

Answer 1

0.9812

Explanation:

Given that human weights are normally distributed with mean 175 and standard deviation 36 pounds

For a sample of 9 people std error of sample would be

`(36)/(√(9) ) =12`

Thus we find that sample mean is N(175, 12)

The plane will lift safely if sample average <200 pounds

i.e. Probability that it can safely lift off (i.e., the average weight of a person in the helicopter is less than 200)

=
`P(\bar x<200) = P(Z<(200-175)/(12) )\\P(Z<2.08)\\=0.5+0.4812\\=0.9812`

~0.981