=Norminv(probability,mean, standard_dev)
is the Inverse of the Cumulative Normal Probability Distribution.
A normal random variable is continuous so the
Cumulative distribution is the integral of the density.
If you don't understand what I meant by integral, you
may need to just know that you need calculus , a
type of math where you study limits, derivatives(rates of change) and integrals(areas of unusual regions)to under
to understand this mathematical formula. Students
who have had no calculus are told to accept the normal
distribution on faith. In that case you will need to read no
further. If you have some calculus, we'll continue.
We'll construct the formula for the standard cumulative normal first. That would be Excel's =NORMINV(x,0,1)
The normal density function for µ=0,σ =1 is
f(x) = [(1/√(2π)] times e^( [-x²/2])
and =NORMINV(x,0,1) = ⌡ f(x) dx integrated from
limits -∞ to x
If µ and σ are any general values then the
density function is
f(x) = [(1/ σ√(2π) ] times e^( [(-1/2)* [(x-µ)/σ]²)
and for the above f(x)
=NORMINV(x,µ,σ) = ⌡ f(x) dx integrated from
limits -∞ to x
You can study the link I've included if you want to see how
calculus applies to statistics if you've had calculus but
never had a calculus based statistics course. .
The normal distribution formula appears near the bottom of
that link .