Question

Until the scale was changed in 1995, SAT scores were based on a scale set many years ago. For Math scores, the mean under the old scale in the 1990s was 470 and the standard deviation was 110. In 2013 the mean was 515 and the standard deviation was 116. Gina took the SAT in 1994 and scored 500 on the Math test. Her cousin Colleen took the SAT in 2013 and scored 530 on the Math test. Who did better relative to their peers, and how can you tell? Group of answer choices Colleen—she scored 30 points higher than Gina. Gina—the standard deviation was bigger in 2013. Gina—her standardized score is higher than Colleen’s. Colleen—her standardized score is higher than Gina’s.

Answer 1

Gina—her standardized score is higher than Colleen’s.

Explanation:

Until the scale was changed in 1995, SAT scores were based on a scale set many years ago.

We solve this question using z score formula also know as standardized score formula which is given as:

z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation.

For Gina

Gina took the SAT in 1994 and scored 500 on the Math test.

For Math scores, the mean under the old scale in the 1990s was 470 and the standard deviation was 110.

x = 500

μ = 470

σ = 110

Hence, the z score is given as:

z = 500 - 470/110

z = 0.27273

Gina's z or standardized score is 0.27273

For Colleen

Her cousin Colleen took the SAT in 2013 and scored 530 on the Math test.

In 2013 the mean was 515 and the standard deviation was 116.

x = 530

μ = 515

σ = 116

Hence, the z score is given as:

z = 530 - 515/116

z = 0.12931

Colleen's z or standardized score is 0.12931

The person who did better relative to their peers is Gina and this is because her standardized score is higher than Colleen’s.