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
Answers
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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