+16 2. Suppose that scores on a knowledge test are normally distributed with a mean of 60 and a standard deviation of 3.4. Scores on an aptitude test are normally distributed with a mean of 110 and a standard deviation of 6.8. Boris scored a 55 on the knowledge test and 106 on the aptitude test. Callie scored 67 on the knowledge test and 119 on the aptitude test.
(a) Which test did Boris perform better on? Use z-scores to support your answer.
(b) Which test did Callie perform better on? Use z-scores to support your answer.
(c) Boris also took a logic test. His z-score on that test was -0.43. Does this change the answer to which test Boris performed better on? Explain your answer using z-scores
+128475 a) (55-60 ) / 3.4 = - 1.47 = .0708
(106 - 110 /6.8 = -.588 ≈ .2810
He did better on the aptitude trst
b) ( 67 - 60) / 3.4 = 2.65 = .996
(119 - 110) / 6.8 = .132 = .5517
She did better on the knowledge test
c ) -.43 = .3336
He did better on the logic test than on the other two tests
