The current age in years of 400 clerical employees at an ins

The current age (in years) of 400 clerical employees at an insurance claims processing center is normally distributed with mean 38 and SD 6. Determine whether the statement below is true or false. If you believe that the statement is false, briefly explain why you think it is false.

A training program for employees under the age of 30 at the center would be expected to attract about 36 employees.

Choose the correct answer below.

A.

False. The center would be expected to attract about 165 employees.

B.

False. The center would be expected to attract about 72 employees.

C.

True.

D.

False. The center would be expected to attract about 148 employees.

Solution

Normal Distribution
Mean ( u ) =38
Standard Deviation ( sd )=6
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P(X < 30) = (30-38)/6
= -8/6= -1.3333
= P ( Z <-1.3333) From Standard Normal Table
= 0.0912                  

For value of n=400 ;
Expected Mean = 9.12*400 = 36.48 ~ 36 It is True

C.

True