Question

practice exercises

1. scores on an sssce social studies paper had a mean of 46. joana obtained a score of 70, giving her a standard score of 3.0. what was the standard deviationof the scores?

a. 3
b. 8
c. 24
d. 72

Explanation:

Step1: Recall the formula for standard score

The formula for standard score (z - score) is \(z=\frac{x-\mu}{\sigma}\), where \(x\) is the raw score, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.

Step2: Substitute the given values into the formula

We are given that \(z = 3.0\), \(x=70\), and \(\mu = 46\). Substituting these into the formula \(z=\frac{x-\mu}{\sigma}\), we get \(3=\frac{70 - 46}{\sigma}\).

Step3: Solve for \(\sigma\)

First, simplify the numerator: \(70-46 = 24\). So the equation becomes \(3=\frac{24}{\sigma}\). Cross - multiply to get \(3\sigma=24\). Then divide both sides by 3: \(\sigma=\frac{24}{3}=8\).

Answer:

B. 8