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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.
\[
z=2.25, \quad x=14.9, \text { and } \sigma=3.2
\]
Answer
Final Answer: The mean, \(\mu\), is \(\boxed{7.7}\).
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 \(\boxed{7.7}\).
