Question

At a local company, the ages of all new employees hired during the last 10 years are normally distributed. The mean age is 34 years old, with a standard deviation of 10 years. Find the percent of new employees that are no more than 40 years old. Round to the nearest percent.

Answer 1

P = 73%

Explanation:

We look for the percentage of employees who are not more than 40 years old.

This is:

`P = (x)/(n) *100\%`

Where x is the number of new employees who are not over 40 years old and n is the total number of new employees.

We do not know the value of x or n. However, the probability of randomly selecting an employee that is not more than 40 years old is equal to
`P = (x)/(n)`

Then we can solve this problem by looking for the probability that a new employee selected at random is not more than 40 years old.

This is:

`P(X< 40)`

Then we find the z-score

`Z = (X - \mu)/(\sigma)`

We know that:

μ = 34 years

`\sigma = 10` years

So

`Z = 0.6`

Then

`P (X<40) = P ((X- \mu)/(\sigma) < (40-34)/(10))\\\\P(X<40) = P(Z<0.6)`

So we have

`P(Z<0.6)`

Looking in the normal standard tables:

`P(Z<0.6)=0.726`

Finally P = 73%