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# If $Z$ is a standard normal variate. Find the value of $c$ for the following $P(0< Z < c)=0.25$

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
• $Z=\large\frac{X-\mu}{\sigma}$
From the table ,
$P(0 < Z < 0.67)=0.2486$
$P(0 < Z <0.68)=0.2518$
$c$ is closer to $0.67$.
We take $c=0.67$