Question

one year, the sat scores had a mean of 1023 and a standard deviation of 213. the act scores had a mean of 20 and a standard deviation of 4.7. mary took the sat exam and received a score of 1344. steve took the act exam and received a score of 26.1. a) what is marys z - score? (round to 2 decimal places) b) what is steves z - score? (round to 2 decimal places) c) who did better, relative to the exam they took? mary steve

Explanation:

Step1: Calculate Mary's z - score

The formula for the z - score is \(z=\frac{x - \mu}{\sigma}\). For Mary, \(x = 134\), \(\mu=102.3\), \(\sigma = 4.7\).

$$z_{Mary}=\frac{134 - 102.3}{4.7}=\frac{31.7}{4.7}\approx6.74$$

Step2: Calculate Steve's z - score

For Steve, assume \(x = 26.1\), \(\mu = 20\), \(\sigma=2.13\)

$$z_{Steve}=\frac{26.1-20}{2.13}=\frac{6.1}{2.13}\approx2.86$$

Step3: Compare z - scores

Since \(z_{Mary}\approx6.74\) and \(z_{Steve}\approx2.86\), and \(6.74>2.86\)

Answer:

A. What is Mary's z - score? \(6.74\)
B. What is Steve's z - score? \(2.86\)
C. Who did better? Mary