# If $Z$ is a standard normal variate. Find the value of $c$ for the following $P(Z > c)=0.85$

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
• $Z=\large\frac{X-\mu}{\sigma}$
$P(Z > c)=0.85$
Since the area > 0.5,the value of c is -ve.
$\therefore P(c < Z < 0)=P(0 < Z < -c)=0.35$
From the table ,
$-c=1.04$
$\Rightarrow c=-1.04$