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.

Question

Mathematics

Colin Bass

10 September, 18:16

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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Answers (1)

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Diego Chambers · Answer 1

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