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7 August, 08:01

Suppose two people, mary and carrie, are up for the same job. mary took the american test of academic ability and received a score of 124 on this test. scores on this test are normally distributed with a mean of 110 and a standard deviation of 8. carrie took the national academic achievement test and received a score of 289. scores on this test are normally distributed with a mean of 250 and a standard deviation of 20. when being considered for the job, both of these tests count equally. find the z score that corresponds to marys test score and the z score that corresponds to carries test score. round to the nearest thousandth.

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  1. 7 August, 09:37
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    Z-scores (left tail) of a given variable X are calculated by

    Z (x) = (x-mean) / standard deviation.

    For Mary:

    Zm (124) = (124-110) / 8=14/8=1.75

    For Carrie:

    Zc (289) = (289-250) / 20=39/20=1.95

    therefore

    Zc>Zm
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