Question

Standardized tests: In a particular year, the mean score on the ACT test was and the standard deviation was . The mean score on the SAT mathematics test was and the standard deviation was . The distributions of both scores were approximately bell-shaped. Round the answers to at least two decimal places.

Find the z-score for an ACT score of 26. The Z-score for an ACT score of 26 is 1.

Answer 1

The Z-score for an ACT score of 26 is 1.26

Explanation:

According to the Question,

• Given that, In a particular year, the mean score on the ACT test was 19.3 and the standard deviation was 5.3, The mean score on the SAT mathematics test was 532 and the standard deviation was 128.

Problems of normally distributed samples(bell-shaped) can be solved using the z-score formula. In a set with mean and standard deviation, the z score of a measure X is given by

Z = (X-μ) / σ

• the z-score for an ACT score of 26. In a particular year, the mean score on the ACT test was 19.3 and the standard deviation was 5.3.

So, Z = (X-μ) / σ

Z = (26 - 19.3) / 5.3

Z = 1.26

The Z-score for an ACT score of 26 is 1.26