Question 1182077: 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 195.3 pounds, with a standard deviation of 61.2 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 by mathmate(429)   (Show Source):
You can put this solution on YOUR website! Given
Weight limit = 9200 lbs
number of passengers and crew, n = 41
mean weight, m = 195.3 lbs
standard deviation, s = 61.2 lbs
Find probability that weight limit will be exceeded with 41 persons on board.
Solution
Maximum mean weight for n = 41 (passengers)
= 9100 / 41 = 221.9512
Standard error of the mean
= standard deviation / sqrt(n)
= 61.2 / sqrt(41)
= 9.557834
z-value when the maximum mean weight will be exceeded
= (221.9512-195.3)/9.557834
= 2.788414 standard errors
P(z>=2.788414)
= 1 - P(z<=2.788414)
= 1 - 0.9973517
= 0.00264834
= 0.2648%
Answer:
the probability that 41 persons on board will overload the plane is 0.265%
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