Very large summation calculator

[Dhamnekar Win,odd]

 In hypergeometric distribution, n= population of n elements, r = sample size, n_{1 =} elements recognized as having some defined criteria, n_{2 =} n - n₁ =  remaining elements other than n₁ . We seek the probability q_k such that the sample size r contain exactly k recognized elements provided [math]k \geq 0, k \leq n_1 [/math] if n₁ is smaller  or [math] k \leq r[/math] if r is smaller. In such a case the probability [math]q_k =\frac{\binom{n_1}{k}\binom{n- n_1}{r - k}}{\binom{n}{r}} \tag {1}[/math]

Now, I want to calculate n=8500, n₁ =1000, r = 1000, k = 0 to 100.  Inserting these values in (1), calculation of summation is very difficult.  In such case, how can I use normal approximation to binomial distribution to find q_k ?

Do you have any clue or hint?

     

Edited April 1, 2022 by Dhamnekar Win,odd

[Genady]

I don't know about the normal approximation in this case, but Excel has HYPGEOMDIST() function...