Question

What is a normal probability curve?

Answer 1

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 `\mu` and spread across from entire real line, although 99.7% is within 3 standard deviations (`\sigma`)

Following is the formula.

`f(x) = \frac {1}{\sqrt {2\pi \sigma ^{2}}} * e^{-{\frac {(x-\mu )^{2}}{2\sigma ^{2}}}}`

Following is an example of a normal probability curve with mean `\mu=0` and standard deviation `\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 `\mu=100` and standard deviation `\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.