Question

A plane filled with students coming home is boarding. The plane's overhead bins can handle at most 2,450 lbs of weight, and are being filled with suitcases that have normally distributed weights of mean 48 lbs and a standard deviation of 14 lbs. If the probability of going over that limit is larger than 0.05, the airline will put all the bags in the cargo hold.

A. if 49 passengers have one bag each, what is the maximum mean weight of a bag?

B. what is the probability of a single bag exceeding the maximum mean weight?

C. what is the probability that the load of 49 bags will exceed the load limit of the plane?

D. should the airline start putting bags in the cargo hold?

Answer 1

a) P( > x) = 0.05

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b) P(X > 51.29)

= P(Z > 0.235)

= 1 - P(Z < 0.235)

= 1 - 0.5929

= 0.4071

c) = 2450/49 = 50

P( > 50)

= P(Z > 1)

= 1 - P(Z < 1)

= 1 - 0.8413

= 0.1587

D) Since the probability in part - C is greater than 0.05, so the airline should start putting bags in the cargo hold.