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The standard normal distribution (Z) is defined as the difference between the value of the variable, X, and the population mean, μ, and the result divided by the population standard deviation, σ.
[tex]Z=\frac{X-\mu}{\sigma}\approx N(0,1)[/tex]For a determined population with normal distribution, the mean is μ=89, the standard deviation is σ=11.5 and the value of the variable is X=82, you can calculate the Z-value as follows:
[tex]\begin{gathered} Z=\frac{82-89}{11.5} \\ Z=\frac{-7}{11.5} \\ Z=-0.608\approx-0.61 \end{gathered}[/tex]The Z-value is -0.61