Answer to Question #310688 in Statistics and Probability for Ron

Question

in a certain university, the students were informed that they need a grade in the top 8% of the engineering students to get a scholarship for the next semester. In the standardization of the test, the mean was 76 and the standard deviation is 14. Assuming that the grade is normally distributed, what must be the minimum grade to obtain the scholarship grant.

Answer 1

$P(Z>z)=0.08 \to P(Z<z)=0.92 \to z=1.41.$

$z=\frac{x-\mu}{\sigma} \to 1.41=\frac{x-76}{14} \to x=1.41*14+76\approx 96.$