On an exam,Tom scored 12 points above the mean and had a z-score of +2.00.The standard deviation for the set of exam scores must be σ = 6.

Question

Quizplus · Accepted Answer

Since Tom's z-score is +2.00, we know that he is 2 standard deviations above the mean. Therefore, if he scored 12 points above the mean, the mean must be 6 points below his score. 
Tom's score = mean + 12
Tom's score - mean = 12
Tom's score - (mean - Tom's score) = 12
2(Tom's score - mean) = 12
Tom's score - mean = 6
So, the mean score is 6 below Tom's score. 
Since the standard deviation is σ = 6, Tom's z-score of +2.00 corresponds to a score that is 2(6) = 12 points above the mean. Therefore, the information given in the question is consistent and the answer is A.

On an Exam,Tom Scored 12 Points Above the Mean and Had