Question

8,900 incoming freshman to a university take an entrance exam, with the top 10% being offered admission to the university's honors program. The average test score is 78%, with a standard deviation of 11%. Use a calculator to find what the student must score to be invited to join the honors program if only 65 scores are looked at to determine the honors admissions requirement.

Answer 1

Answer:

The student must score 79.75% to be invited to join the honors program.

Step-by-step explanation:

Let X denote the score of a freshman in the entrance exam.

It is provided that the average test score is 78%, with a standard deviation of 11%.

It is provided that the top 10% being offered admission to the university's honors program.

Let x denote the score eligible for being offered admission to the university's honors program.

Then, P (X ≤ x) = 0.90.

Then P (Z < z) = 0.90.

The corresponding z-score is, 1.28.

*Use a z-table.

Compute the value of x as follows:

$z=\frac{x-\mu}{\sigma/\sqrt{n}}\\\\1.28=\frac{x-78}{11/\sqrt{65}}\\\\x=78+(1.28\times \frac{11}{\sqrt{65}})\\\\x=79.75\%$

Thus, the student must score 79.75% to be invited to join the honors program.