Standardized tests: In a particular year, the mean score on the ACT test was 21.

Question

Standardized tests: In a particular year, the mean score on the ACT test was 21.8 and standard deviation was 5.7. The mean score on the SAT mathematics test was 533 and standard deviation was 121. The distributions of both scores were approximately bell- Round the answers to two decimal places. Find the z-score for an ACT score of 16. The z-score for an ACT score of 16 is Find the z-score for a SAT math score of 524. The z-score for a SAT math score of 524 is Jose's ACT score had a z -score of 2.02. What was his ACT score? Jose's ACT score is Emma's SAT score had a z -score of -0.9. What was her SAT score? Emma's SAT score is

Explanation / Answer

Part 1:
mu = 21.8 and sigma = 5.7
z-score for x=16 can be calculated using central limit theorem
z = (x - mu)/sigma = (16 - 21.8)/5.7 = -1.0175

Part 2:
mu = 533 and sigma = 121
z-score for x=524 can be calculated using central limit theorem
z=(x-mu)/sigma = (524 - 533)/121 = -0.0744

Part 3:
mu = 21.8 and sigma = 5.7
for z=2.02, find x using central limit theorem
z = (x - mu)/sigma
x = z*sigma + mu = 2.02*5.7 + 21.8 = 33.314

Part 4:

mu = 533 and sigma = 121
for z=-0.9, find x using central limit theorem
z = (x - mu)/sigma
x = z*sigma + mu = -0.9*121 + 533 = 424.1

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