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?

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

Step-by-step 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.

For this problem, we have that:

Uniformly distributed between 14 minutes and 30 minutes, which means that

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

This is . So

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