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?

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,

Therefore,Cutoff far a failing score is 49.

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

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

Therefore, percentage of students failed is 2.28%.

a. the residual plot for model 1 has a random pattern and is a good fit for the data.