The SAT is an exam that is used by many universities for admission. Suppose that the scores on the SAT mathematics exam have a normal distri

Question

The SAT is an exam that is used by many universities for admission. Suppose that the scores on the SAT mathematics exam have a normal distribution with mean 500 and standard deviation of 100. The statistics department identified students scoring in the top 4% of the SAT mathematics exam for recruitment. About what is the cutoff score for recruitment by the statistics department

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Claire 2 months 2021-10-09T03:14:43+00:00 1 Answer 0 views 0

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    2021-10-09T03:15:56+00:00

    Answer:

    The cutoff score for recruitment by the statistics department is 675.

    Step-by-step explanation:

    Problems of normally distributed samples can be solved using the z-score formula.

    In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

    Z = \frac{X - \mu}{\sigma}

    The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

    In this problem, we have that:

    \mu = 500, \sigma = 100

    Cutoff score for the top 4%.

    100-4 = 96th percentile, which is X when Z has a pvalue of 0.96. So X when Z = 1.75.

    Z = \frac{X - \mu}{\sigma}

    1.75 = \frac{X - 500}{100}

    X - 500 = 1.75*100

    X = 675

    The cutoff score for recruitment by the statistics department is 675.

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45:7+7-4:2-5:5*4+35:2 =? ( )