Question

determine which score corresponds to the higher relative position.

1. which is better, a score of 92 on a test with a mean of 71 and a standard deviation of 15, or a score of 688 on a test with a mean of 493 and a standard deviation of 150?

a) a score of 688
b) both scores have the same relative position.
c) a score of 92

Explanation:

Step1: Calculate the z - score for the first score

The formula for the z - score is \(z=\frac{x-\mu}{\sigma}\), where \(x\) is the score, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.
For \(x = 92\), \(\mu=71\), \(\sigma = 15\)
\(z_1=\frac{92 - 71}{15}=\frac{21}{15}=1.4\)

Step2: Calculate the z - score for the second score

For \(x = 688\), \(\mu = 493\), \(\sigma=150\)
\(z_2=\frac{688 - 493}{150}=\frac{195}{150}=1.3\)

Answer:

C. A score of 92