The weight of luggage carried onto a plane by passengers is normally distributed
ID: 2506554 • Letter: T
Question
The weight of luggage carried onto a plane by passengers is normally distributed with a mean
of 20 KG and a standard deviation of 6 KG.
a. What is the probability that a passenger's luggage weighs 25 KG?
b. Passengers are "fast-tracked" if they have luggage weighing less than 10 KG. What percentage of
passengers are fast tracked?
c. The airline wants to set the maximum weight limit so that only 2.5% of passengers have to pay an
overweight luggage fee. What limit should it set?
d. If the plane has 100 passengers, what is the probability that the average weight of their luggage is
less than 23 KG?
Explanation / Answer
a) z = (X-mean)/Standard deviation
Here probability for weight equals to 25kg will be zero because it's a point and would have infinitesimally small probability.
b) z= (10-20)/6 = -1.667
Probability from standard normal table corresponding to z= -1.667 is eqaul to 0.04846
For tables, refer to
https://www.stat.tamu.edu/~lzhou/stat302/standardnormaltable.pdf
Percentage of passengers fast tracked = Probability*100 % = 0.04846*100 = 4.846%
c) z value corresponding to top 2.5% (1-2.5/100) is equal to 1.96
Let x kg be the maximum weight limit
1.96 = (x-20)/6
x= 31.76
d) z = (23-20)/6 = 0.5
Probability = 0.6914
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