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

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

To find : True/False. for 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  = 1  =>  84.13 %  

=> People above 44 age = 100 - 84.13 =  15.87%  ≈  63    out of 400

Z score for 38  = (38 - 38)/6 = 0 => 50%

Hence People between 38 & 44  age = 84.13 - 50 = 34.13 % ≈  137 out of 400

Hence 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

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

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