Question

Before every​ flight, the pilot must verify that the total weight of the load is less than the maximum allowable load for the aircraft. The aircraft can carry 41 ​passengers, and a flight has fuel and baggage that allows for a total passenger load of 6 comma 683 lb. The pilot sees that the plane is full and all passengers are men. The aircraft will be overloaded if the mean weight of the passengers is greater than StartFraction 6 comma 683 l b Over 41 EndFraction equals 163 lb. What is the probability that the aircraft is​ overloaded? Should the pilot take any action to correct for an overloaded​ aircraft? Assume that weights of men are normally distributed with a mean of 180.5 lb and a standard deviation of 38.2.

Answer 1

Answer:

The probability that the plane is oveloaded is P=0.9983.

The pilot should take out the baggage and send it in another plain or have less passengers in the plain to not overload.

Step-by-step explanation:

The aircraft will be overloaded if the mean weight of the passengers is greater than 163 lb.

If the plane is full, we have 41 men in the plane. This is our sample size.

The weights of men are normally distributed with a mean of 180.5 lb and a standard deviation of 38.2.

So the mean of the sample is 180.5 lb (equal to the population mean).

The standard deviation is:

$\sigma=\frac{\sigma}{\sqrt{N}} =\frac{38.2}{\sqrt{41}}=\frac{38.2}{6.4} =5.97$

Then, we can calculate the z value for x=163 lb.

$z=\frac{x-\mu}{\sigma}=\frac{163-180.5}{5.97}=\frac{-17.5}{5.97}= -2.93$

The probability that the mean weight of the men in the airplane is below 163 lb is P=0.0017

$P(\bar X<163)=P(z<-2.93)=0.00169$

Then the probability that the plane is oveloaded is P=0.9983:

$P(overloaded)=1-P(X<163)=1-0.0017=0.9983$

The pilot should take out the baggage or have less passengers in the plain to not overload.