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# If $Z$ is a standard normal variate. Find the value of $c$ for the following $P(-c < Z < c)=0.40$

Toolbox:
• Standard normal distribution:
• In a standard normal distribution $\mu=0,\sigma ^2=1$
• The random variable $X$ can be converted to the standard normal variable $Z$ by the transformation
• $Z=\large\frac{X-\mu}{\sigma}$
$P(-c < Z < c)=0.40$
By symmetry,
$2P(0 < Z < c)=0.40$
$\Rightarrow P(0 < Z < c)=0.20$
From the table $c=0.52$ and $-c=-0.52$