Question

The current age (in years) of 400 clerical employees at an insurance claims processing center is normally distributed with mean  = 38 and Standard deviation  =6. For each statement below, please specify True/False. If false, briefly explain why. A. More employees at the processing center are older than 44 than between 38 and 44. B. A training program for employees under the age of 30 at the center would be expected to attract about 36 employees.

Answer 1

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Answer 2

The current age (in years) of 400 clerical employees at an insurance claims processing center is normally distributed with mean 38 & SD = 6 .

Step-by-Step Explanation:

A. More employees at the processing center are older than 44 than between 38 and 44.

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

Solution:

Mean = 38

SD = 6

Z score = (Value - Mean)/SD  

Z score for 44  = (44 - 38)/6  

                          = 6/6

                          =  1  

                          =  84.13 %  

People above 44 age = 100 - 84.13

                                     =  15.87% = 63  out of 400

Z score for 38  = (38 - 38)/6 = 0/6 = 0

                          = 50%

Hence People between 38 & 44  age = 84.13 - 50

                                                                 =  34.13%  = 137 out of 400

A. Therefore, More employees at the processing center are older than 44 than between 38 and 44 is FALSE .

Z score for 30  = (30 - 38)/6 =  -1.33  =  9.15 %  

                                               = 36 out of 400

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