Answer:
0.9812
Step-by-step 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
[tex]\frac{36}{\sqrt{9} } =12[/tex]
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)
= [tex]P(\bar x<200) = P(Z<\frac{200-175}{12} )\\P(Z<2.08)\\=0.5+0.4812\\=0.9812[/tex]
~0.981