Incorrect probability density [closed]

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I'm trying to make a bell curve (normal gauss distribution). I have some problems regarding the probability density curve, since its values are so low. If you look column N in the attached file - I used the NORMDIST command. Values should be somewhere between 0,2 and 0,4 - but they're about 100x lower.

link to xlsx file

Does anyone knows the reason for this?

Regards, Gašper

Answer 1

The results from NORM.DIST are correct... if you directly implement the Gaussian function in your sheet using:

=(1/($F$8*SQRT(2*PI())))EXP( -((M3-$F$7)^2)/(2$F$8^2))

which is an implementation of the standard Gaussian function e.g. f(x) on:

http://mathworld.wolfram.com/GaussianFunction.html

then the results exactly match Excel's NORM.DIST built in function.

When you say the values "should be" in range 0.2-0.4 I'm not sure you can be correct, because you have a Gaussian distribution with mean=261.6379 and std. dev=164.8153. That is a very widely stretched Gaussian distribution, and remember the area under a Gaussian must always sum to 1, so it makes sense that the values you're using i.e. range [-200,200] falling within around 1 standard deviation will be very small under that density function.

Put another way, the maximum value you will find under a Gaussian distribution will be at it's mean. Your mean is 261 so if I put 261 in your column titled "X" (column M) I will get the largest possible value I can hope for. This is 0.002. And you say you are expecting values 0.2-0.4. This is impossible given the standard deviation (164) you are using. If your standard deviation was 100 times smaller you might be getting towards that kind of value.