Question

1.) 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 42 ​passengers, and a flight has fuel and baggage that allows for a total passenger load of 6,846 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 6,846 lb/42=164 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 183 lb and a standard deviation of 36.8. lb. (a & b)

a.) What is the probability that the aircraft is​ overloaded?

b.) Should the pilot take any action to correct for an overloaded​ aircraft? Assume that weights of men are normally distributed with a mean of 183.5 lb and a standard deviation of 36.2.

2.) Suppose that an airline uses a seat width of 16.9 in. Assume men have hip breadths that are normally distributed with a mean of 14.5 in. and a standard deviation of 1.1 in. Complete parts​ (a) through​ (c) below.

​(a) Find the probability that if an individual man is randomly​ selected, his hip breadth will be greater than 16.9 in.

​(b) If a plane is filled with 114 randomly selected​ men, find the probability that these men have a mean hip breadth greater than 16.9 in. ​

(c) Which result should be considered for any changes in seat​ design: the result from part​ (a) or part​ (b)?

Answer 1