Question

1. a score that is 10 points above the mean corresponds to a z - score of z = +1.20. what is the sample standard deviation?

Explanation:

Step1: Recall z - score formula

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. We know that $x-\mu = 10$ (since the score is 10 points above the mean) and $z = 1.20$.

Step2: Solve for standard deviation

We can re - arrange the z - score formula to solve for $\sigma$. From $z=\frac{x - \mu}{\sigma}$, we get $\sigma=\frac{x-\mu}{z}$. Substitute $x-\mu = 10$ and $z = 1.20$ into the formula.
$\sigma=\frac{10}{1.20}=\frac{100}{12}=\frac{25}{3}\approx8.33$

Answer:

$\frac{25}{3}\approx8.33$