Z-scores have four very important functions as follows: They divide an acceptabl
ID: 3152277 • Letter: Z
Question
Z-scores have four very important functions as follows: They divide an acceptably symmetrical curve into known percentages. They locate individual positions in a distribution very precisely. They locate positions of two or more individuals in the same distribution very precisely one to the other. For mathematical purposes, they provide a common scale for disparate interval and/or ratio measures. As Chief Pilot of a major airline, you are interested in a way to compare pilot performance on an aviation knowledge test. Since there are two different tests that the pilots may take, you want to be able to fairly compare their scores. One of the exams has a score scale from 0 to 150 and another with a score scale of 50 to 300. Describe how you would use z-scores to be able to compare performance of individual pilots.
Explanation / Answer
Answer:
Form the comparison purpose of the two tests for the pilot; we need to use the z-scores for the both tests. The more z-score describes the more score. For the first test the range is given as 0 to 150 and for the second test the range is given as 50 to 300. We assume that the scores are distributed normally. Then for the first test for the individual pilot we can find the z score and then we can compare this z-score with the z-score of the second test. If the z score for first test is more than the z-score for the second test, then we can say that the pilot have more proficiency in the first test. If the z-score for second test is more then we can conclude that the pilot have more proficiency in the second test as compared to first test.
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