Eduardo wrote:
I find using the 2 Excel worksheet functions below
LOGNORMDIST(4, 3.5, 1.2) = 0.039084
NORMSDIST((LN(4 / 3.5)) / 1.2) = 0.5443013
The 2 results above do not obey the relation stated in excel
Help for LOGNORMDIST:

I think it does if you correct your NORMSDIST formula accordingly.
I believe the correct formula is NORMSDIST( (ln(4) - 3.5) / 1.2 ) or
NORMSDIST( ln(4/exp(3.5)) / 1.2 ).

This is because for LOGNORMDIST, the 2nd and 3rd parameters
are the mean (m) and sd (s) of ln(x), not x. Thus, m = ln(m') and
m' = exp(m), where m' is the mean of x. So ln(x)-ln(m') = ln(x/m') =
ln(x/exp(m)), and ln(a)/s = ln(a^(1/s)).

Help for LOGNORMDIST:
LOGNORMDIST(x, μ, σ) = NORMSDIST((ln(x) - ln(μ)) / σ)
I corrected the right hand side of the above equality from the
one given in Excel Help: NORMSDIST((ln(x) - μ) / σ)

What version of Excel are you using? Your corrected expression
matches the help text that I see for Office Excel 2003.