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Comparing Two Different Normal Distributions

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Kerri scores 677 on the SAT math test which has a mean of 500 and a standard deviation of 100. Kyle scores 28 on the ACT math test which has a mean of 18 and a standard deviation of 6. Assuming that both tests measure the same kind of ability, who has the higher score? If grading were done on a curve, what would their respective percentages be?

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Solution Summary

This solution shows how to compare values selected from two different normal distributions.

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We must assume for this problem that both the SAT and the ACT scores follow a normal distribution. Any observation from a normal distribution has a corresponding "standardized" score or "z-score" which tells the distance of the observation from the mean in units of standard ...

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