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.
Answer:
The probability that the weight limit will be exceeded when there are exactly 41 passengers and 3 crew members on board is;
0.253
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