# standardized scores & percentile answers and explanation

__Standardized
Scores & Percentile__ Step by step Solution with
Explanation

__Standardized Scores & Percentile__Step by step Solution with Explanation

## Your question:

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

__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)**.