Question

The scores on a final exam were approximately normally distributed with a mean of 82 and a standard deviation of 11. If 85 students took the exam, and above a 60 is a passing grade, how many students failed the exam?

A. 13

B. 1

C. 2

D. 12

Answer 1

The scores on a final exam were approximately normally distributed with a mean of 82 and a standard deviation of 11. If 85 students took the exam, and above a 60 is a passing grade, the students failed in the exam are C. 2.

Answer 2

2 students failed in the final exam.

Explanation:

The scores on a final exam were approximately normally distributed.

We know that,

`Z=(X-\mu)/(\sigma)`

X = raw score = 60

μ = mean = 82

σ = standard deviation = 11

Putting the values,

`Z=(60-82)/(11)=-2`

From Normal distribution table, we get

`P(-2)=0.0227=2.27\%`

Hence, 2.27% of 85 students failed the final exam.

So the number of students who failed the exam is,

`=85* 0.0227=1.9295\approx 2`