Question

At a local company, the ages of all new employees hired during the last 10 years are normally distributed. The mean age is 38 years old, with a standard deviation of 10 years. Find the percent of new employees that are no more than 30 years old. Round to the nearest percent.

Answer 1

Answer:

P = 21%

Step-by-step explanation:

We look for the percentage of employees who are not more than 30 years old.

This is:

$P = \frac{x}{n} *100\%$

Where x is the number of new employees who are not over 30 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 30 years old is equal to $P = \frac{x}{n}$

Then we can solve this problem by looking for the probability that a new employee is not more than 30 years old.

This is:

$P(X< 30)$

Then we find the z-score

$Z = \frac{X - \mu}{\sigma}$

We know that:

μ = 38 years

$\sigma = 10$ years

So

$Z = -0.8$

Then

$P (X$

By symmetry of the distribution

$P(Z0.8)$

Looking in the normal standard tables

$P(Z>0.8)=0.211$

Finally P = 21%