Question

A study of the time spent shopping in a supermarket for a market basket of 20 specific items showed an approximately uniform distribution between 20 and 40 minutes. What is the probability that the shopping time will be between 25 and 30 minutes? (round to two decimal places) Answer What is the probability that the shopping time will be less than 35 minutes? (round to two decimal places) Answer What is the mean? Answer What is the standard deviation of shopping time? (round to two decimal places)

Answer 1

By CDF of Uniform distribution, where X ~ Unif(a , b)

P(x1 < X < x2) = (x2 - x1) / (b - a)

P(X < x) = (x - a) / (b - a)

Mean = (a + b) / 2

Standard deviation = (b - a) / $\sqrt{12}$

Probability that the shopping time will be between 25 and 30 minutes = (30 - 25) / (40 - 20) = 0.25

Probability that the shopping time will be less than 35 minutes = (35 - 20) / (40 - 20) = 0.75

Mean = (40 + 20) / 2 = 30 minutes

Standard deviation of shopping time = (40 - 20) / $\sqrt{12}$ = 5.77 minutes