NORMDIST function is not giving the correct output
distribution, excel, excel-formula, normal-distribution, statistics
Solution
A probability cannot have values greater than 1, but a density can.
The integral of the entire range of a density function is equal 1, but it can have values greater than one in specific interval. Example, a uniform distribution on the interval [0, ½] has probability density f(x) = 2 for 0 ≤ x ≤ ½ and f(x) = 0 elsewhere. See below:
`=NORMDIST(x, mean, dev, FALSE)` returns the density function. Densities are probabilities per unit. It is almost the probability of a point, but with a very tiny range interval (the derivative in the point).
shg's answer here, explain how to get a probability on a given interval with NORMIDIST and also in what occasions it can return a density greater than 1.
For a continuous variable, the probability of any particular value is zero, because there are an infinite number of values.
If you want to know the probability that a continuous random variable with a normal distribution falls in the range of a to b, use:
=NORMDIST(b, mean, dev, TRUE) - NORMDIST(a, mean, dev, TRUE)
The peak value of the density function occurs at the mean (i.e., =NORMDIST(mean, mean, dev, FALSE) ), and the value is:
=1/(SQRT(2*PI())*dev)
The peak value will exceed 1 when the deviation is less than 1 / sqrt(2pi) ~ 0.399,
which was your case.
This is an amazing answer on Cross Validated Stack Exchange (statistics) from a moderator (whuber), that addresses this issue very thoughtfully.
Problem
I'm trying to use `NORMDIST` function in Excel to create a bell curve, but the output is strange. My mean is `0,0000583` and standard deviation is `0,0100323` so when I plug this to the function `NORMDIST(0,0000583; 0,0000583; 0,0100323; FALSE)` I expect to get something close to `0,5` as I'm using the same value as the mean probability of this value should be `50%`, but the function gives an output of `39,77` which is clearly not correct. Why is it like this?