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.)

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slicergiza slicergiza · Answer 1 · 2019-08-22T13:44:40+02:00

Answer:

The cutoff for a failing score was 40,

Approximately 2.3% of the students failed.

Step-by-step explanation:

Given,

Mean, [tex]\mu=60[/tex]

Standard deviation, [tex]\sigma=10[/tex]

Let x represents the cutoff for a failing score,

Thus, according to the question,

[tex]\frac{x-\mu}{\sigma}=-2[/tex]

[tex]\frac{x-60}{10}=-2[/tex]

[tex]x-60=-20[/tex]

[tex]x=-20+60[/tex]

[tex]x=40[/tex]

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. 