Assume two people, Mary and Carrie, are up for the same job. Mary took The American Test of Academic Ability as well as received a score of 124 on this test. Scores upon this test are normally distributed with the mean of 110 and standard deviation of 8. Carrie took The National Academic Achievement Test and received score of 289. Scores upon this test are normally distributed with mean of 250 and a standard deviation of 20. When being considered for job, both of these tests count equally.
Determine the z score that corresponds to Mary's test score and the z score that corresponds to Carrie's test score. Round to the nearest thousandth.