Question

Airline passenger travel light, others heavy. Assume that the weight of the carrry on bags is uniformly distributed between 4 and 24 pounds.

1. What is median weight of airline bags?

2. How much would a carry on bag weigh in the 80th percentile?

3. Computer interquartile weight of carry on bags

4. A carry on bag weighs 15 pounds . in what quartile is it?

Answer 1

a) Median weight = (4 + 24)/2 = 14

b) Let 80th percentile is x. Then:

(x - 4) / (24 - 4) = 0.80

x - 4 = 16

x = 20

c) 75th percentile:

(x - 4) / (24 - 4) = 0.75

x = 19

25th percentile:

(y - 4) / (24 - 4) = 0.25

y = 9

Hence,

Interquartile weight = 75th percentile - 25th percentile = 19 - 9 = 10

d) Percentile for 15 pounds = (15 - 4) / (24 - 4) = 11/20 = 0.55