Before every flight, the pilot must verify that the total weight a 6,308 Ib. The pilot sees that the plane is full and all passenge pilot take any action to correct for an overloaded aircraft? Ass The probability is approximately. (Round to four decimal places as needed.)

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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 38 passengers, and a flight has fuel and baggage that allows for a total passenger load of
6,308 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
6,308 lb
= 166 lb. What is the probability that the aircraft is overloaded? Should the
%3D
pilot take any action to correct for an overloaded aircraft? Assume that weights of men are normally distributed with a mean of 174.1 Ib and a standard deviation of 36.2.
38
The probability is approximately
(Round to four decimal places as needed.)
Should the pilot take any action to correct for an overloaded aircraft?
O A. Yes. Because the probability is high, the pilot should take action by somehow reducing the weight of the aircraft.
B. No. Because the probability is high, the aircraft is safe to fly with its current load.
Transcribed Image Text:Help 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 38 passengers, and a flight has fuel and baggage that allows for a total passenger load of 6,308 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 6,308 lb = 166 lb. What is the probability that the aircraft is overloaded? Should the %3D pilot take any action to correct for an overloaded aircraft? Assume that weights of men are normally distributed with a mean of 174.1 Ib and a standard deviation of 36.2. 38 The probability is approximately (Round to four decimal places as needed.) Should the pilot take any action to correct for an overloaded aircraft? O A. Yes. Because the probability is high, the pilot should take action by somehow reducing the weight of the aircraft. B. No. Because the probability is high, the aircraft is safe to fly with its current load.
Expert Solution
Step 1

Let X be a random variable that denotes the weights of men.

Here it is given that -

mean(μ) = 174.1

standard deviation (δ) = 36.2

total number of observations = 38

As X belongs to normal distribution-

X~N(174.1,36.22)

Z = 38(X¯-174.1)36.2~N(0,1)

 

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