Answer to Question #196465 in Statistics and Probability for Kendall

Question

The applicant to a company took a 60 item entrance exam. Their scores resemble a normal distribution with a mean of 50 and a standard deviation of 4. If the company would like to have the top 20 percent of the applicant to go on to the next phase of the application process, what should be their cut-off score in exam?

Answer 1

$\mu=50,\sigma=4,n=60$

The z-score for top 20% exam is -

$z_{0.2}=0.8416$

The cutoff\minimum score for the exam-

$=\mu+z_{0.2}\sigma$

$=50+0.8416\times 4\\[9pt]=50+3.3664\\[9pt]=53.3664$