e-Statistics

Normal Density Function

It is determined by two parameters $\mu =$ and $\sigma =$ . The common shape of the normal density function is often described as “bell-shaped” curve.

Provided the normal PDF, we can predict the chance that an observation from the distribution is between a= and b= . We calculate such a probability, denoted by , as the area under the curve over the range between a and b.

$\displaystyle P(a \le X \le b) = \Phi\left(\frac{b-\mu}{\sigma}\right) - \Phi\left(\frac{a-\mu}{\sigma}\right)$ =

In order to compute the probability $P(-\infty < X < b)$ or $P(a < X < \infty)$ in the form above, you must use the symbol a=-Inf or b=+Inf in appropriate boxes to indicate $a=-\infty$ or $b=+\infty$ .