Question

A study of the time spent shopping at a supermarket is for a basket with 20 specific items showed an approximately a uniform distribution between 20 minutes and 40 minutes. What is the probability that the shopping time will be:

Answer 1

The probability that the shopping time will be between 25 and 30 minutes is 0.25.

Explanation:

The question is:

What is the probability that the shopping time will be between 25 and 30 minutes?

Solution:

Let X represent the time spent shopping at a supermarket for a basket with 20 specific items.

It is provided that X follows Uniform (20, 40).

Compute the probability that the shopping time will be between 25 and 30 minutes as follows:

`P(25<X<30)=\int\limits^(30)_(25) {(1)/(40-20)} \, dx`

`=\int\limits^(30)_(25) {(1)/(20)} \, dx \\\\=(1)/(20)* [x]^(30)_(25)\\\\=(30-25)/(20)\\\\=0.25`

Thus, the probability that the shopping time will be between 25 and 30 minutes is 0.25.