One professor teaches a large section, section A, of a particular class, and on the first test of the term, the test scores in section A were approximately normally distributed with a mean of 78 and a standard deviation of 6. Another professor also teaches a large section, section B, of the same class, and on the first test of the term, the test scores in section B were also approximately normally distributed with a mean of 74 and a standard deviation of 10.
Two students, one from each section, earned a grade of 92 on the exam. The student from section B claims that he did better because the section B test, with a mean of 74, was obviously more difficult than the section A test with a mean of 78. However, the student from section A claims that because she has a higher z-score, she actually performed "better." Calculate the z-scores for each student's test grade and settle their dispute; that is, decide who had the superior performance on this test.
The solution provides step by step method for the calculation of Z score. Formula for the calculation and Interpretations of the results are also included.