Question

The scores on a psychology exam were normally distributed with a mean of 60 and a standard deviation of 10 . 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? The cutoff for a failing score was nothing . ​(Simplify your​ answer.) Approximately nothing percent of the students failed. ​(Round to one decimal place as​ needed.)

Answer 1

The cutoff for a failing score was 40,

Approximately 2.3% of the students failed. ​

Explanation:

Given,

Mean,
`\mu=60`

Standard deviation,
`\sigma=10`

Let x represents the cutoff for a failing score,

Thus, according to the question,

`(x-\mu)/(\sigma)=-2`

`(x-60)/(10)=-2`

`x-60=-20`

`x=-20+60`

`x=40`

Thus, the cutoff for a failing score is 40,

∵ P(<-2) = 0.02275 = 2.275 % ≈ 2.3 %

Hence, Approximately 2.3 % of the students failed. ​