Suppose the random variable x is best described by a normal distribution with $\mathbf{\mu }\mathbf{=}\mathbf{30}$ and $\mathbf{\sigma }\mathbf{=}\mathbf{4}$. Find the z-score that corresponds to each of the following x values:

$$\begin{gathered} \mathbf{a}\mathbf{.}\mathbf{x}\mathbf{=}\mathbf{20}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{b}\mathbf{.}\mathbf{x}\mathbf{=}\mathbf{30} \\ \mathbf{c}\mathbf{.}\mathbf{x}\mathbf{=}\mathbf{2}\mathbf{.}\mathbf{75}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{d}\mathbf{.}\mathbf{x}\mathbf{=}\mathbf{15} \\ \mathbf{e}\mathbf{.}\mathbf{x}\mathbf{=}\mathbf{35}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{f}\mathbf{.}\mathbf{x}\mathbf{=}\mathbf{25} \end{gathered}$$

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