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# What is value of X such that P(-X < Z < X)=0.95?

Jan 23, 2017

$- 2.575 < Z < 2.575$

#### Explanation:

$T o t a l p r o b a b i l i t y = 1$

then,
$1 - 0.95 = 0.5$

divide by 2, $\frac{0.5}{2} = 0.025$

From normal distribution table, we found that $P \left(Z < 0.025\right) = 2.575$
Therefore
$P \left(- X < Z < X\right) = 0.95$
$= P \left(- 2.575 < X < 2.575\right)$