Question

The scores on a psychology exam were normally distributed with a mean of 57

and a standard deviation of 4. A failing grade on the exam was anything 2 or more standard deviations below the mean. What was the cutoff for a failing​ score? Approximately what percentage of the students​ failed?

Answer 1

Cutoff for a failing score is 49 and 2.28% students failed.

Explanation:

We have been given that scores on a psychology exam were normally distributed with a mean of 57 and a standard deviation of 4.

2 standard deviation below mean would be,

`57-2(4) =57-8= 49`

Therefore,Cutoff far a failing score is 49.

Now let us find out the z-score for our given values,

`z=(x-\mu)/(\sigma)`

`z=(49-57)/(4)=(-8)/(4) =-2`

Now let us look up the probability from normal distribution table.

`P(z<-2) =0.02275`

Therefore, percentage of students failed is 2.28%.