If RAND() returns a number less than 0.00034, your formula

will return a negative number, and if RAND() returns a number greater
than 0.99966, your formula will return a number greater than 23. Up to
the OP to decide whether this is OK or not.


Hi. I may be wrong, but I think you used a Standard Deviation of Sqrt(23/2) instead of Sqrt(23/12).
It's easier for me to test this with another program.

equ = InverseCDF[NormalDistribution[23/2, Sqrt[23/2]], x];

At machine precision, we get the two solutions you mention...

NSolve[equ == 0, x]

{x - 0.000347981}

NSolve[equ == 23, x]

{x - 0.999652}

If we do 1-million sums of 23 Random numbers(0-1), the Standard Deviation on this test data is 1.38..

m = Tr /@ RandomReal[1, {1000000, 23}];
{Min[m], Mean[m], Max[m], StandardDeviation[m]}

{4.68429, 11.5014, 18.0794, 1.38515}

Which checks with joeu2004's solution:

Sqrt[23/12.]

1.38444

And what we would expect...

Sqrt[23.] (UniformDistribution[{0, 1}] // StandardDeviation)

1.38444

--
HTH :)
Dana DeLouis


"Harlan Grove" wrote in message ...

joeu2004 wrote...
...

=norminv(rand(), 23/2, sqrt(23/12))

...

According to the CLT, the sum is a normal distribution regardless of
the distribution of the individual random variables being summed. The
distribution of the sum has a mean of N*m and a std dev of sqrt(N)*s,
where N is the number of random variables summed, and "m" and "s" are
the mean and std dev of each of the N random variables.

...

Not quite. The sum of iid random variables is ASYMPTOTICALLY normal.
Meaning, the distribution of the sum of N iid random variables becomes
normal as N approaches infinity. For smallish values of N, the normal
distribution is a rough approximation of the actual distribution of
the sum.

Also, the normal distribution with mean 23/2 and standard deviation
23/2 has a finite probability of NEGATIVE values and values GREATER
THAN 23. If RAND() returns a number less than 0.00034, your formula
will return a negative number, and if RAND() returns a number greater
than 0.99966, your formula will return a number greater than 23. Up to
the OP to decide whether this is OK or not.