Question

Part One

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 comma 7626,762 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 762 l b Over 42 EndFraction equals 161 6,762 lb 42=161 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 183 lb and a standard deviation of 38.2. The probability is approximately nothing. ​(Round to four decimal places as​ needed.)

Should the pilot take any action to correct for an overloaded​ aircraft?

A. No. Because the probability is​ high, the aircraft is safe to fly with its current load.

B. Yes. Because the probability is​ high, the pilot should take action by somehow reducing the weight of the aircraft.

Part two

An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between

140 lb and 191 lb. The new population of pilots has normally distributed weights with a mean of

150 lband a standard deviation of 28.3 lb

a. If a pilot is randomly​ selected, find the probability that his weight is between

140 lb and 191

lb.The probability is approximately

​(Round to four decimal places as​ needed.)b. If 35 different pilots are randomly​ selected, find the probability that their mean weight is between 140

lb and 191

lb.The probability is approximately

​(Round to four decimal places as​ needed.)

c. When redesigning the ejection​ seat, which probability is more​ relevant?

A.

Part​ (a) because the seat performance for a single pilot is more important.

B.

Part​ (a) because the seat performance for a sample of pilots is more important.

C.

Part​ (b) because the seat performance for a single pilot is more important.

D.

Part​ (b) because the seat performance for a sample of pilots is more important

Answer 1