If $X \sim N(\mu,\sigma^2)$, then $Z^2=\left(\frac{X-\mu}{\sigma}\right)^2$ is…

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If $X \sim N(\mu,\sigma^2)$, then $Z^2=\left(\frac{X-\mu}{\sigma}\right)^2$ is a Chi-square variate with

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$Z=\frac{X-\mu}{\sigma} \sim N(0,1)$

Square of standard normal variable follows $\chi^2$ distribution with 1 d.f.

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