SOLUTION: Jacob scores 16 on the ACT. Emily scores 670 on the SAT. The ACT scores for more than 1 million students in the same class were roughly normal with mean of 20.8 and

Question 1064645: Jacob scores 16 on the ACT. Emily scores 670 on the SAT. The ACT scores for more
than 1 million students in the same class were roughly normal with mean of 20.8
and standard deviation of 4.8. The SAT scores for 1.4 million students in a recent
graduating class were roughly normal with a mean of 1026 and standard deviation of
209.
(a) Compute the z-scores for Jacob and Emily.
(b) Sketch the two standardized normal curves for Jacob and Emily.
(c) Assuming that both tests measure scholastic aptitude, who has the higher score?
Sketch a standardized normal curve that indicates your solution.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Jacob scores 16 on the ACT. Emily scores 670 on the SAT.
The ACT scores for morethan 1 million students in the same class were roughlynormal with mean of 20.8 and standard deviation of 4.8.
The SAT scores for 1.4 million students in a recent
graduating class were roughly normal with a mean of 1026
and standard deviation of 209.
(a) Compute the z-scores for Jacob and Emily.
Jacob:: z(16) = (16-20.8)/4.8 = -1
Emily:: z(670) = (670-1026)/209 = -1.7033
(b) Sketch the two standardized normal curves for Jacob and Emily.
(c) Assuming that both tests measure scholastic aptitude, who has the higher score?
Ans:: -1 > -1.7033 ; Jacob
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Sketch a standardized normal curve that indicates your solution.
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Cheers,
Stan H.
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