Question

An employer gives a pre-employment evaluation to a large group of applicants.
The scores for the evaluation are normally distributed with a mean of 154 and a standard deviation of 21.

a) What percentage of applicants will score more than 160 on the evaluation?

b) The employer wants to interview only those applicants who score in the top 15%.
What should the cut-off score be for the interviews? Round to the nearest whole number.

Answer 1

Solution :

X: The scores for the evaluation

mean = 154

standard deviation = 21

a) What percentage of applicants will score more than 160 on the evaluation?

P(score more than 160 on the evaluation) = P(x>160)

= P( (x-mean)/standard deviation > (160-154)/21 )

= P ( z > 0.29 ) = 1 - P ( Z < 0.29 )

= 1 - 0.6141

= 0.3859

Answer : 0.3859

b) The employer wants to interview only those applicants who score in the top 15%.
What should the cut-off score be for the interviews? Round to the nearest whole number.

for top 15% , z = 1.04

x = z*standard deviation + mean = 1.04*21 + 154 = 176

Answer : 176