- Save \& Exit Certify Lesson: 6.2 The Standard Normal Distribut... Question 5 of 10, Step 1 of 1 $4 / 10$ Correct Use the $z$-score formula, $z=\frac{x-\mu}{\sigma}$, and the information below to find the mean, $\mu$. Round your answer to one decimal place, if necessary. \[ z=2.25, \quad x=14.9, \text { and } \sigma=3.2 \]

Step 1 ：We are given the z-score formula, \(z=\frac{x-\mu}{\sigma}\), where \(z\) is the z-score, \(x\) is the value, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.

Step 2 ：We are given \(z=2.25\), \(x=14.9\), and \(\sigma=3.2\).

Step 3 ：We can rearrange the formula to solve for \(\mu\): \(\mu = x - z\sigma\).

Step 4 ：Substituting the given values into the equation, we get \(\mu = 14.9 - 2.25*3.2\).

Step 5 ：Solving the equation, we find that \(\mu = 7.7\).

Step 6 ：Final Answer: The mean, \(\mu\), is \(\boxed{7.7}\).