Normdist Problem

[Rodby]

I put in the following:
X=-.055762
Mean=.005
SD=.04
Cumulative=FALSE =>means probability mass function, not cumulative
The result displayed is 3.14615427

The result makes no sense to me. Any result over one makes no sense to me.

I reviewed the answer from a previous thread (Jerry W. Lewis, 8/3/2006) that
continuous functions do not have a probability mass, but rather a pdf, an
integral over a tiny range around -.055, but the Excel function result still
makes no sense.

What am I missing here?

 

[David Biddulph]

With cumulative=FALSE, aren't you looking at a density function? In other
words if the cumulative probability is P, you are looking at the
differential dP/dx.
Because you have a very small value of SD, the value of P is going from 0 to
1 across a very narrow range of x values, so the gradient is very large (and
can happily go beyond 1). It is the *cumulative* probability that can't
exceed 1, not the probability density.

You can easily check the calculation of the probability density function.
If X is in A1, mean in A2, and SD in A3, the density is
=(1/(SQRT(2*PI())*A3))*EXP(-((A1-A2)^2/(2*A3^2)))
You'll see the formula in Excel help for NORMDIST, or in any stats textbook.

 

[David Biddulph]

With cumulative=FALSE, aren't you looking at a density function? In other
words if the cumulative probability is P, you are looking at the
differential dP/dx.
Because you have a very small value of SD, the value of P is going from 0 to
1 across a very narrow range of x values, so the gradient is very large (and
can happily go beyond 1). It is the *cumulative* probability that can't
exceed 1, not the probability density.

You can easily check the calculation of the probability density function.
If X is in A1, mean in A2, and SD in A3, the density is
=(1/(SQRT(2*PI())*A3))*EXP(-((A1-A2)^2/(2*A3^2)))
You'll see the formula in Excel help for NORMDIST, or in any stats textbook.