SOLUTION: ON a recent grade 11 math contest, the mean score was 57.9 with a standard deviation of 11.6 On the grade 10 math contest written the same day the mean score was 61.2 with a sta

Question 1176963: ON a recent grade 11 math contest, the mean score was 57.9 with a standard deviation of 11.6
On the grade 10 math contest written the same day the mean score was 61.2 with a standard deviation of 11.9
Tom scored 84.3 on the grade 11 contest and his friend Jen scored 86.2 on the grade 10 contest. Make an argument in favour of Toms results being better than his friend Jens.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Tom was (84.3-57.9)/11.6 for +2.28 z-score or 2.28 sd above the mean
Jens was (86.2-61.2)/11.9 for +2.10 z-score
Both scores were far above the mean, and Tom's is slightly further from the mean than Jens's were. This is about 0.65 of a single percentile, however, so it is not a major difference.
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