Question

for a population with a standard deviation of $sigma = 12$, a score of $x = 115$ corresponds to $z=+1.25$. what is the population mean?

Explanation:

Step1: Recall the z - score formula

The z - score formula is $z=\frac{X-\mu}{\sigma}$, where $z$ is the z - score, $X$ is the raw score, $\mu$ is the population mean, and $\sigma$ is the population standard deviation.

Step2: Rearrange the formula to solve for $\mu$

Starting from $z=\frac{X - \mu}{\sigma}$, we can multiply both sides by $\sigma$: $z\sigma=X-\mu$. Then, we can rewrite it as $\mu=X - z\sigma$.

Step3: Substitute the given values

We are given that $X = 115$, $z = 1.25$, and $\sigma=12$. Substitute these values into the formula $\mu=X - z\sigma$. So, $\mu=115-1.25\times12$.

Step4: Calculate the value of $\mu$

First, calculate $1.25\times12 = 15$. Then, $\mu=115 - 15=100$.

Answer:

100