When flying, the average weight of passengers’ carry-on luggage in the overhead

Question

When flying, the average weight of passengers’ carry-on luggage in the overhead bins is 14 lb with a standard deviation of 3 lb.

a)  126 people will be boarding an airplane and placing their carry-on luggage in the overhead compartments. If the maximum weight these compartments can support is 1800 lb, what can you say about the probability that all the bags can be safely stowed overhead?

b) Upon reaching their destination, the 126 passengers will be boarding 7 smaller commuter airplanes that will each hold 18 people, and whose overhead bins will support 250 lbs. What can you say about successfully stowing all the bags overhead in any given airplane?

c)  What assumptions have you made?

d) What role does the Central Limit Theorem play in defining the reliability of your answers to parts a and b of this question?

Explanation / Answer

mean = 14 and sd = 3
a)
For 126 people, mean = 126*14 = 1764
and sd = 3*sqrt(126) = 33.6749

P(X < 1800)
= P(z < (1800 - 1764)/33.6749)
= P(z < 1.0690)
= 0.8575

b)
For 18 people, mean = 18*14 = 252
and sd = 3*sqrt(18) = 12.7279

P(X < 250)
= P(z < (250 - 252)/12.7279)
= P(z < -0.1571)
= 0.4376

c)
Assumpation made is the weight of bags are normally distributed

d)
Using central limit theorem, value of z is calculated which is further used to calculate the value of probability

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