# Find th critical for the middle 50%. Don't unstandardize.

Question
Math Word Problem
Find th critical for the middle 50%. Don't unstandardize.

2021-01-16
$$\displaystyle\mu={53.9}$$
$$\displaystyle\sigma={28.5}$$
proportion= 0.5000
proportion left 0.5000 is equally distributed both left and right side of normal curve
z value at $$\displaystyle{0.25}=\pm{0.674}{\left(\frac{{0.50}}{{2}}\right)}$$
$$\displaystyle{z}=\frac{{{x}-\mu}}{\sigma}$$
so, $$\displaystyle{X}={z}\sigma+\mu=$$
$$\displaystyle{X}{1}=-{0.674}\cdot{28.5}+{53.9}={34.68}$$
$$\displaystyle{X}{2}={0.674}\cdot{28.5}+{53.9}={73.12}$$

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