Interpreting Z-Scores?

SAT scores are an example of standardized tests that allow us to compare results of students from around the country. Suppose the mean score of a student who takes the SAT scores a 520 on the Math portion, with σ=12 points. The mean English score is 535 with σ=14 points.

What does it mean if a student’s score on the English portion has a z-score of 1.5?

If a student’s z-score for the Math was +1.4 and their English score was +1.6, on which portion did they score better relative to all other students?

Find the actual test scores for the z-scores from problem (b).

If Avery scores a 510 on the Math and a 508 on the English, on which section did she score better relative to all students in the country?

Find the and of the combined scores for Math + English.

Use part e to find and interpret the z-score for a student who scored an 1150 overall.

Use part e to find and interpret the z-score for a student who scored a 1000 overall.

 Test A has a mean score of 45 with a standard deviation of 3.5 and test B has a mean score and standard deviation of 20 and 1.75, respectively. Ralph scored a 50 on test A, and Louise scored a 22 on test B. Who had the better score?

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