Question

Suppose the amount of time needed to change the oil in a car is uniformly distributed between 14 minutes and 30 minutes, with a mean of 22 minutes and a standard deviation of 4.6 minutes.

Let X represent the amount of time, in minutes, needed to complete a randomly selected oil change. What is the probability that a randomly selected oil change takes at most 20 minutes to complete?

Answer 1

37.5% probability that a randomly selected oil change takes at most 20 minutes to complete.

Explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X lower than x is given by the following formula.

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

For this problem, we have that:

Uniformly distributed between 14 minutes and 30 minutes, which means that
`a = 14, b = 30`

What is the probability that a randomly selected oil change takes at most 20 minutes to complete?

This is
`P(X \leq 20)`. So

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

`P(X \leq 20) = (20 - 14)/(30 - 14) = 0.375`

There is a 37.5% probability that a randomly selected oil change takes at most 20 minutes to complete.