Question

A) A college accepts the top 5% of the students who took the entrance exam. The distribution of exam scores is approximately normal with a mean of 71 points and standard deviation of 9 points. You achieved 84 points on the exam. What is your percentile? Will you be accepted? Explain.

B) Using this same data, assume that you achieved 87 points on the exam. What is your percentile? Will you be accepted? Explain.

Answer 1

(A)

= 71

= 9

Z = (84- 71)/9 = 1.44

Table of Area Under Standard Normal Curve gives area = 0.4251

So,

84 points = (0.5 + 0.4251) X100 = 92.51 %

So, my percentile = 92.51.

This is not within top 5%.

So, I will not be accepted.

(B)

= 71

= 9

Z = (87- 71)/9 = 1.78

Table of Area Under Standard Normal Curve gives area = 0.4625

So,

84 points = (0.5 + 0.4625) X100 = 96.25 %

So, my percentile = 96.25.

This is within top 5%.

So, I will be accepted.