Question

suppose your statistics professor reports test grades as z - scores, and you got a score of 2.20 on an exam. write a sentence explaining what that means.
select the correct choice below.
a. the score was 2.20 points lower than the mean score in the class.
b. the score was 2.20 standard deviations lower than the mean score in the class.
c. the score was 2.20 points higher than the mean score in the class.
d. the score was 2.20 standard deviations higher than the mean score in the class.

Explanation:

Step1: Recall the definition of z - score

The z - score formula is \(z=\frac{x - \mu}{\sigma}\), where \(x\) is the raw score, \(\mu\) is the mean, and \(\sigma\) is the standard deviation. A positive z - score means \(x>\mu\) and a negative z - score means \(x < \mu\). The magnitude of the z - score represents the number of standard deviations from the mean.

Step2: Analyze the given z - score

Since the z - score is \(z = 2.20\) (a positive value). Using the formula \(z=\frac{x-\mu}{\sigma}\), when \(z>0\), we have \(x-\mu=z\sigma\). Here \(z = 2.20\), which means \(x=\mu + 2.20\sigma\)

Answer:

D. The score was 2.20 standard deviations higher than the mean score in the class.