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# Standardized Scores & Percentile Step by step Solution with Explanation

ETS (Educational Testing Service) provides information about the GRE (Graduate Record Examination) Subject Tests. For the Biology Subject Test, the scores are normally distributed with a mean score of 616 and a standard deviation of 115. For the History Subject Test, the scores are normally distributed with a mean score of 496 and a standard deviation of 76.

Haley took the History Subject Test and received a score of 550. Find the standardized score (z-score) for Haley.

E. -0.57

Bill took the Biology Subject Test and received a score of 600. Find the percentile corresponding to Bill's score on the Biology Subject Test.

Ε. 6.81%

When comparing raw scores, Bill scored higher than Haley. When comparing standardized scores, who (Bill or Haley) scored higher compared to other examinees taking the same Subject Test?

# Standardized Scores & Percentile Answers and Explanation

We can calculate the z-score (standardized score) for Haley using the following formula:

z = (X - μ) / σ

Plugging in the values:

z = (550 - 496) / 76

However, the answer choices provide clues. We can see that options A, B, C, and D represent percentiles between 6.81% and 91.31%. Since the normal distribution is symmetrical, a score of 600 (which is closer to the mean than 616) would likely correspond to a percentile above 50%.

Therefore, Bill's percentile on the Biology Subject Test is most likely C) 78.52%.

• Bill's raw score is higher than the mean (616), but we don't know his exact z-score.

Since a positive z-score indicates scoring above the mean, and Haley's z-score is positive, we can conclude that Haley scored higher than Bill relative to other examinees taking the same Subject Test (Option B).

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