Question

​The scores on a psychology exam were normally distributed with a mean of 58 and a standard deviation of 6. A failing grade on the exam was anything 2 or more standard deviation below the mean. What was the cutoff for a failing score? Approximately what percentage of the students failed?

The cutoff for a failing score was ____

Simplify answer)

Approximately ___ percent of the students failed

( Round to one decimal place as needed)

Answer 1

Solution:

Given: The scores on a psychology examination were normally distributed with a mean of = 58 and a standard deviation of .

Part a)

A failing grade on the examination was anything 2 or more standard deviation below the mean.

That is: If X =  The scores on a psychology examination is less than 2 standard deviations below mean is a failing grade.

Thus find x value by using following formula:

Thus the cutoff for a failing score was 46

Part b) Approximately what percentage of the students failed?

That is find:

P( X < 46) =.......?

Thus:

P( X < 46) = P( Z< -2.00)

Look in z table for z = -2.0 and 0.00 and find corresponding area.

P( Z< -2.00) = 0.0228

Thus

P( X < 46) = P( Z< -2.00)

P( X < 46) = 0.0228

P( X < 46) = 2.28%

P( X < 46) = 2.3%

Thus approximately 2.3 percent of the students failed