Certain transportation company has a fleet of 210 vehicles. The average age of the vehicles is 4.25 years, with a standard deviation of 18 months. In a random sample of 40 vehicles, what is the probability that the average age of vehicles in the sample will be less than 4 years

And we can find the following probability:

And the last probability can be founded using  the normal standard distribution or excel.

Step-by-step explanation:

For this case we define the random variable X as the ages of vehicles. We know the following info for this variable:

represent the mean

represent the deviation in years

They select a sample size of n=40>30. And they want to find this probability:

Since the sample size is large enough we can use the central limit theorem and the distribution for the sample mean would be:

We can use the z score formula given by:

And if we find the z score for 4 we got:

And we can find the following probability:

And the last probability can be founded using  the normal standard distribution or excel.

a negative exponent is translated as follows:

so, we have