Question

Assume a random variable representing the amount of time it takes for a customer service representative to pick up has a uniform distribution between 15 and 20 minutes. What is the probability that a randomly selected application from this distribution took less than 18 minutes

Answer 1

0.6 = 60% probability that a randomly selected application from this distribution took less than 18 minutes.

Explanation:

Uniform probability distribution:

An uniform distribution has two bounds, a and b.

The probability of finding a value of at lower than x is:

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

The probability of finding a value between c and d is:

`P(c \leq X \leq d) = (d - c)/(b - a)`

The probability of finding a value above x is:

`P(X > x) = (b - x)/(b - a)`

Uniform distribution between 15 and 20 minutes.

This means that
`a = 15, b = 20`

What is the probability that a randomly selected application from this distribution took less than 18 minutes?

`P(X < 18) = (18 - 15)/(20 - 15) = 0.6`

0.6 = 60% probability that a randomly selected application from this distribution took less than 18 minutes.