# SAT and ACT

Scores by women on the SAT-I test are normally distributed with a mean of 998 and a standard deviation of 202. Scores by women on the ACT test are normally distributed with a mean of 20.9 and a standard deviation of 4.6. Assume that the two tests use different scales to measure the same aptitude.

a. If a women gets a SAT score that is the 67th percentile, find her actual SAT score and her equivalent ACT score

b. If a woman gets a SAT score of 1220, find her equivalent ACT score.

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#### Solution Summary

Scores by women on the SAT-I test are normally distributed with a mean of 998 and a standard deviation of 202. Scores by women on the ACT test are normally distributed with a mean of 20.9 and a standard deviation of 4.6. Assume that the two tests use different scales to measure the same aptitude.

a. If a women gets a SAT score that is the 67th percentile, find her actual SAT score and her equivalent ACT score

b. If a woman gets a SAT score of 1220, find her equivalent ACT score.