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

Answer:

The cutoff for a failing score was 40,

Approximately 2.3% of the students failed. ​

Step-by-step explanation:

Given,

Mean, $\mu=60$

Standard deviation, $\sigma=10$

Let x represents the cutoff for a failing score,

Thus, according to the question,

$\frac{x-\mu}{\sigma}=-2$

$\frac{x-60}{10}=-2$

$x-60=-20$

$x=-20+60$

$x=40$

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. ​