What is a normal probability curve?

1 Answer
soq
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 #\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.

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