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

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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 ,
$-c=1.04$
$\Rightarrow c=-1.04$
answered Sep 19, 2013 by sreemathi.v
 

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