Respuesta :
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:
[tex]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\%[/tex]
Thus, the student must score 79.75% to be invited to join the honors program.
