# What is a normal probability curve?

Dec 21, 2017

Normal probability curve is the plot of probability density function of the normal distribution. This probability curve is bell shaped, has a peak at mean $\setminus \mu$ and spread across from entire real line, although 99.7% is within 3 standard deviations ($\setminus \sigma$)

Following is the formula.

$f \left(x\right) = \setminus \frac{1}{\setminus \sqrt{2 \setminus \pi \setminus {\sigma}^{2}}} \cdot {e}^{- \left\{\setminus \frac{{\left(x - \setminus \mu\right)}^{2}}{2 \setminus {\sigma}^{2}}\right\}}$

Following is an example of a normal probability curve with mean $\setminus \mu = 0$ and standard deviation $\setminus \sigma = 1$

graph{1/sqrt(2*pi) * (e^((-x^2)/2)) [-4, 4, -0.2, 0.5]}

Following is an example of a normal probability curve with mean $\setminus \mu = 100$ and standard deviation $\setminus \sigma = 15$

graph{1/sqrt(2pi15^2) * (e^((-(x-100)^2)/(2*15^2))) [40, 160, -0.007, 0.05]}

It might be hard to notice but the second graph is a lot more spread out.