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The scores on a psychology exam were normally distributed with a mean of 57 and a...

The scores on a psychology exam were normally distributed with a mean of 57 and a standard deviation of 8. 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______? (Simplify your answer)

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Answer #1

Sol:

The cutoff for a failing score was=mean-2*sd

=57-2*8

=57-16

=41

P(X<=41)

P(Z<=41-57/8)

P(Z<-2)

=1-P(Z<2)

=1-0.9772

=0.0228

=0.0228*100

=2.28%

Approximately 2.28 percentage of the students​ failed

ANSWERS:

The cutoff for a failing score=41

Approximately 2.28 percentage of the students​ failed

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