Question

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

Answer 1

Answer:

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

Step-by-step 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,

$z=\frac{x-\mu}{\sigma}$

$z=\frac{49-57}{4}=\frac{-8}{4} =-2$

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

$P(z$

Therefore, percentage of students failed is 2.28%.