The maximum weight for a checked baggage at an airport is 50 lb per bag and the

Question

The maximum weight for a checked baggage at an airport is 50 lb per bag and the charge for an overweight bag (between 50 lb and 70 lb) is $100 CAD. A research conducted a study and its results showed that the mean weight of luggage checked by a randomly selected economy-class passenger flying between two cities on a certain airline is 40 lb, and the standard deviation is 10 lb. he mean and standard deviation for a business-class passenger are 30 lb and 6 lb, respectively. Suppose luggage weights are independent. a) What is the proportion of overweight baggages for economy-class fights? b) If there are 12 business-class passengers and 50 economy-class passengers on a particular flight, determine the expected value and standard deviation of total luggage weight. c) What is the probability that the total weight of 50 baggages from 50 economy-class passengers is at most 2050 lb? d) If the weight of baggages from a business-class is normally distributed, what is the probability that a randomly selected baggage is overweight?

Explanation / Answer

a) P(X>50) =P(Z>(50-40)/10) =1-P(Z<1)=1-0.8413=0.1587

b)expected value =12*30+50*40=2360

and std deviation =6*(12)1/2+10*(50)1/2 =91.495

c)P(X<2050)=P(Z<(2050-2360)/91.495)=P(Z<-3.388)=0.0004

d)P(X>50)=P(Z>(50-30)/6)=1-P(Z<3.333)=1-0.9996=0.0004

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