At a local company, the ages of all new employees hired during the last 10 years are normally distributed. the mean age is 35 years old, with a standard deviation of 10 years.

if you were to take a sampling of 10 employees, what is the probability your mean age will be at least 37? round to the nearest percent.

P =26%

Step-by-step explanation:

In this problem we have the ages of all new employees hired during the last 10 years of normally distributed.

We know that the mean is years and standard deviation is years

By definition we know that if we take a sample of size n of a population with normal distribution, then the sample will also have a normal distribution with a mean

And with standard deviation

Then the average of the sample will be

And the standard deviation of the sample will be

Now we look for the probability that the mean of the sample is greater than or equal to 37.

This is

To find this probability we find the Z-score

So

We know that

Looking in the normal table we have:

Finally P = 26%