Question

Your company gives everyone who applies to your company a proficiency test. Your boss likes to hire people who fall in the "average" range. They feel that people who score exceptionally high on the test are more likely to leave for a better job, and people who score very low are not productive enough. The average score on the proficiency test is 750 with a variance of 400. Your boss tell you to exclude the top 14% and the bottom 27%of applicants. What range of scores would get an interview?

What is the larger Z? What is the smaller Z? What is μ?   What is σ ? What is the larger X? What is the small X?   What is your conclusion?   

Answer 1

Result:

Your company gives everyone who applies to your company a proficiency test. Your boss likes to hire people who fall in the "average" range. They feel that people who score exceptionally high on the test are more likely to leave for a better job, and people who score very low are not productive enough. The average score on the proficiency test is 750 with a variance of 400. Your boss tell you to exclude the top 14% and the bottom 27%of applicants. What range of scores would get an interview?

What is the larger Z?

Larger z= 1.08

(Excel function used to get z value: =NORM.S.INV(0.14), for upper tail value take the positive value)

What is the smaller Z?

Smaller z = -0.613

(Excel function used to get z value: =NORM.S.INV(0.27))

What is μ?

μ=750

What is σ ?

σ = 20

What is the larger X?

X= mean+z*sd = 750+1.08*20

=771.60

What is the small X?

X= mean+z*sd = 750-0.613*20

=737.74

What is your conclusion?   

The range of scores would get an interview are from 737.74 to 771.60.