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 43 passengers, and a flight has fuel and baggage that allows for a total passenger load of 7,181 lb. The pilot 7,181 lb 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 = 167 Ib. What is the probability that the aircraft is overloaded? Should the pilot take any action to correct for an 43 overloaded aircraft? Assume that weights of men are normally distributed with a mean of 178.9 lb and a standard deviation of 35.4. The probability is approximately. (Round to four decimal places as needed.)

College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....
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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 43 passengers, and a flight has fuel and baggage that allows for a total passenger load of 7,181 Ib. The pilot
7,181 lb
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
- = 167 Ib. What is the probability that the aircraft is overloaded? Should the pilot take any action to correct for an
43
overloaded aircraft? Assume that weights of men are normally distributed with a mean of 178.9 lb and a standard deviation of 35.4.
The probability is approximately
(Round to four decimal places as needed.)
Transcribed Image Text: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 43 passengers, and a flight has fuel and baggage that allows for a total passenger load of 7,181 Ib. The pilot 7,181 lb 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 - = 167 Ib. What is the probability that the aircraft is overloaded? Should the pilot take any action to correct for an 43 overloaded aircraft? Assume that weights of men are normally distributed with a mean of 178.9 lb and a standard deviation of 35.4. The probability is approximately (Round to four decimal places as needed.)
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