The scores on a university examination are Normally distributed with a mean of 62 and a standard
deviation of 11. If the bottom 5% of students will fail the course, what is the lowest mark that a
student can have and still be awarded a passing grade?
A) 62 B) 57 C) 44 D) 40

how do i get this answer?

Question

The scores on a university examination are Normally distributed with a mean of 62 and a standard
deviation of 11. If the bottom 5% of students will fail the course, what is the lowest mark that a
student can have and still be awarded a passing grade?
A) 62 B) 57 C) 44 D) 40

how do i get this answer?

directrix · Answer

C) 44 is what I cranked out.

z = (x - 62)/11

5% is associate with a z-score of -1.64

-1.64 = (x-62)/11

x = 43.96