How to find the value of K?

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How to find the value of $K$? If $z$ has a standard normal distribution, find $k$ (to $4$ significant figures) if $P(-k < z < k)$ = $0.329$

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If $\Phi$ is the cdf for the standard normal distribution, $\Phi(-k) = 1 - \Phi(k)$, so you want $\Phi(k) - \Phi(-k) = 2 \Phi(k) - 1 = 0.329$, or $\Phi(k) = 1.329/2$. Look it up or use software.