A small jet can carry up to passengers and crew members. There is a weight restriction of pounds on board. The combined weight of each passenger (or crew member) and his luggage has a mean of pounds, with a standard deviation of pounds. What is the probability that the weight limit will be exceeded when there are exactly passengers and crew members on board? Carry your intermediate computations to at least four decimal places. Report your result to at least three decimal places.

Complete Question:

A small jet can carry up to 41 passengers and 3 crew members. There is a weight restriction of 9200 pounds on board. The combined weight of each passenger (or crew member) and his luggage has a mean of 197.9 pounds, with a standard deviation of 64.1 pounds. What is the probability that the weight limit will be exceeded when there are exactly 41 passengers and 3 crew members on board? Carry your intermediate computations to at least four decimal places. Report your result to at least three decimal places.

The probability that the weight limit will be exceeded when there are exactly 41 passengers and 3 crew members on board is;

0.253

Step-by-step explanation:

a) Data and Calculations:

Capacity of the small jet = 41 passengers and 3 crew members = 44

Weight restriction = 9,200 pounds

Mean of the combined weight of passengers and crew = 8,707.6 (44 * 197.9) pounds

Weight's standard deviation = 2,802.4 (44 * 64.1) pounds

Excessive weight total = 11,528 (8,707.6 + 2,802.4)

Excess weight = Excessive weight total minus Total Weight Restriction

=2,328 (11,528 - 9,200)

Probability of exceeding weight limit = Excess weight/Weight restriction

= 2,328/9,200

= 0.253