Question #d87c1

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Answer 1 · 2016-02-20T19:16:14

If 25% lies in the middle of the distribution, 75% must lie outside it.

Also, $\frac{75 %}{2} = 37.5 %$ $(75%)/2=37.5%$ lies to the left of -z or more simply, #37.5%+25%=62.5% lies to the left of z ...

Now use a Standard Normal Table to look up z:

$P (Z < z) = 0.625$ $P(Zltz)=0.625$

$z = 0.319$ $z=0.319$

And, because the Standard Normal is perfectly symmetric ...

$- z = - 0.319$ $-z=-0.319$

Now, check the answer ...

$P (- 0.319 < z < 0.319) = 0.25$ $P(-0.319< z < 0.319)= 0.25$

hope that helped