I was trying to experiment some stuff (scaling issues and hypothesis testing) with normal distribution. While doing so, I found out that :
NORM.S.DIST(0, FALSE), which takes Z-value, returns prob. mass function (PMF) = 0.398942
When I use X= (Stand. Dev)*Z + Mean; for Mean = 12; SD = 2, X = 12 for Mean =12
But, =NORM.DIST(12,Mean = 2,SD = 2,FALSE), I get prob. mass function (PMF) = 0.19947114.
Essentially, norm.dist gives 1/2 the figure from norm.s.dist. How could this be possible? However, this doesn’t happen for cumulative distrib. function. I got the same value using both the functions. I am not sure why EXCEL is behaving erratically for calculating PMF?
Is this an error?
Can someone please help?
Thanks in advance.
The reason it is giving half the value is that it should give half the value.
If the standard deviation is twice the size, then the graph of the probability function is twice the "width". But the area under the probability function is always 1, so all the heights must be divided by 2 in order to maintain the area at 1.
So probability density functions' heights at matching points change, even though areas between matching points don't. Basically, if you multiply the standard deviation by m, then all the values of the probability function must be divided by m.
The following website has an interactive applet that will allow you to see what happens to a normal distribution's height when you change the mean and/or standard deviation. https://www.geogebratube.org/student/b77653#material/60983
Note that in this case it is not called a "probability mass function". Since the variable is continuous, it's called a "probability density function".