Question

1. for a given set of data, the standard score, z, corresponding to the raw score, x, is given by z = (x - μ)/σ, where μ is the mean of the set and σ is the standard deviation. if, for a set of scores, μ = 78 and σ = 6, which of the following is the raw score, x, corresponding to z = 2? f. 90 g. 84 h. 80 j. 76 k. 66

Explanation:

Step1: Rearrange the z - score formula

Given $z=\frac{x - \mu}{\sigma}$, we can solve for $x$. Multiply both sides of the equation by $\sigma$: $z\sigma=x - \mu$. Then add $\mu$ to both sides to get $x=z\sigma+\mu$.

Step2: Substitute the given values

We know that $z = 2$, $\mu=78$, and $\sigma = 6$. Substitute these values into the formula $x=z\sigma+\mu$. So $x=2\times6 + 78$.

Step3: Calculate the value of x

First, calculate $2\times6=12$. Then $x=12 + 78=90$.

Answer:

F. 90