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30 January, 00:10

The scores on a psychology exam were normally distributed with a mean of 56 and a standard deviation of 6. 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?

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  1. 30 January, 03:44
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    32 and 47.5%

    Step-by-step explanation:

    Given that X-scores on a psychology exam were normal

    X:N (56,6)

    Failing grade is 2 or more std deviations below the mean

    Mean = 56

    2 std deviations = 12

    Mean-2 std dev = 56-2 (12)

    =56-24

    =32

    Hence failing score cutoff is 32

    I. e. if a student scores less than 32, he is deemed to have failed in the exam

    Percentage of students failed = 100*P (X<32)

    = P (Z<-2)

    =100 (0.475)

    =47.5%

    =
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