Use the formula for finding a $z$-score to determine the missing value in the following table. Round your answer to two decimal places, if necessary.
\begin{tabular}{|c|c|c|c|}
\hline $\boldsymbol{z}$ & $\boldsymbol{x}$ & $\boldsymbol{\mu}$ & $\boldsymbol{\sigma}$ \\
\hline-2.48 & $?$ & 42.80 & 3.08 \\
\hline
\end{tabular}
Answer
Final Answer: The missing value in the table is \(\boxed{35.16}\).
Step 1 ：We are given the z-score, the mean, and the standard deviation, and we are asked to find the value from the data set. The formula for finding a z-score is given by: \(z = \frac{x - \mu}{\sigma}\). We can rearrange the formula to solve for x: \(x = z \cdot \sigma + \mu\).
Step 2 ：Substitute the given values into the formula: \(z = -2.48\), \(\mu = 42.8\), \(\sigma = 3.08\).
Step 3 ：Calculate the value of x: \(x = -2.48 \cdot 3.08 + 42.8 = 35.1616\).
Step 4 ：Round the final answer to two decimal places: \(x = 35.16\).
Step 5 ：Final Answer: The missing value in the table is \(\boxed{35.16}\).
