The first Stats exam had a mean of 65 and a standard deviation of 10 points: the

Question

The first Stats exam had a mean of 65 and a standard deviation of 10 points: the second had a mean of 80 and a standard deviation of 5 points. Derrick scored an 80 on both tests. Julie scored a 75 on the first test and a 85 on the second. They both totaled 160 points on the two exams, but Julie claims that her total is better. Explain. Select the correct choice below and, if necessary fill in the answer boxes within your choice. (Round to three decimal places as needed.) A) Julie's claim is correct. Derrick's z-scores are 1.5 for the first test and 0 for the second test. Julie's z-scores are 5 for the first test and 2 for the second test. Derrick's total is 1.5, which is less than Julie's total 2.5. B) Julie's claim is incorrect. Derrick's z-scores are 1.5 for the first test and 0 for the second test. Julie's z-scores are 5 for the first test and 2 for the second test. Derrick's total is 1.5, which is more than Julie's total, 2.5. C) Julie's claim is incorrect. They both totaled 160 points on the two exams so neither student did better than the other.

Explanation / Answer

The objective here is to standardize their scores for both tests with z-scores using the formula z = (x - mean)/sd:

Derrick's first examination z = (80 - 65)/10 = 1.5

Derrick's second examination z = (80 - 80)/5 = 0

His combined z-score is 1.5

Julie's first examination z = (75 - 65)/10 = 1

Julie's second examination z = (85 - 80)/5 = 1

Julie's combined z-score is 2, so Julie's total is better than Derrick's. I hope that helps!

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