Question

(j) william has a standardized score of 0.754. how tall is he? 0.754 = \frac{x - 170.636}{8.438} \longrightarrow x = 176.998 william is 176.998

Explanation:

Step1: Recall z - score formula

The z - score formula is $z=\frac{x - \mu}{\sigma}$, where $z$ is the standardized score, $x$ is the value we want to find, $\mu$ is the mean, and $\sigma$ is the standard deviation. Here, $z = 0.754$, $\mu=170.636$, and $\sigma = 8.438$.

Step2: Solve for $x$

We start with the equation $0.754=\frac{x - 170.636}{8.438}$. Multiply both sides by $8.438$: $0.754\times8.438=x - 170.636$. Then $6.352252=x - 170.636$. Add $170.636$ to both sides: $x=6.352252 + 170.636=176.988252\approx176.998$.

Answer:

$176.998$