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

Answer:

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

Step-by-step 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:

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

                         $=\int\limits^{30}_{25} {\frac{1}{20}} \, dx \\\\=\frac{1}{20}\times [x]^{30}_{25}\\\\=\frac{30-25}{20}\\\\=0.25$

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