Explanation
We are given the following:
[tex]\begin{gathered} z=0.64 \\ x=-34.90 \\ \sigma=9.48 \end{gathered}[/tex]
We are required to determine the missing value μ.
This is achieved thus:
We know that the formula for z-score is given as:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Therefore, we have:
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ 0.64=\frac{-34.90-\mu}{9.48} \\ \text{ Cross multiply } \\ -34.90-\mu=0.64\times9.48 \\ -34.90-\mu=6.0672 \\ -\mu=6.0672+34.90 \\ -\mu=40.9672 \\ \mu=-40.9672 \\ \mu\approx-40.97 \end{gathered}[/tex]
Hence, the answer is:
[tex]\mu\approx-40.97[/tex]
