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SAT scores have a mean of 1026 and a standard deviation of 209. ACT scores have...

SAT scores have a mean of 1026 and a standard deviation of 209. ACT scores have a mean of 20.8 and a standard deviation of 4.8. A student takes both tests while a junior and scores 860 on the SAT and 16 on the ACT. Compare the scores.

Math   Statistics-And-Probability   
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Answer #1

Convert both to z-scores so you can compare them on the same scale.

Z = (x - μ) / σ

z(860) = (860-1026)/209 = -0.7943

P(Z < -0.7943) = 0.2135

Z(16)  = (16-20.8)/4.8 = - 1.00

P(Z < -1) = 0.1587

scores 860 on the SAT is higher than the 16 on the ACT.

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