Question

which score has a higher relative position, 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? (1 point) both scores have the same relative position. a score of 688 a score of 92

Explanation:

Step1: Calculate z - score for score of 92

The formula for the z - score is \(z=\frac{x-\mu}{\sigma}\), where \(x\) is the data point, \(\mu\) 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 z - score for score of 688

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

Answer:

A score of 92