Hey i got this question, and suppose to do it with excel, Does the hypergeometri
ID: 2929226 • Letter: H
Question
Hey i got this question, and suppose to do it with excel,
Does the hypergeometric approach the Binomial?
Thanks
Suppose a population contains a finite number N of elements that possess one of two characteristics. Thus, r of the elements might be of one type (for example type A) and N-r are of another type (for example type B). A sample of n elements is randomly selected from the population, and the random variable of interest is Y, the number of type A elements in the sample. Then Y has a hypergeometric distribution and we know. PC y) = Now let denote by p, the probability of a randomly selected element is of type A. Then, p r/N. Let's assume as N increases, r will also change in the fixed proportion to it in such a way to keep p fixed (i.e. r = N*p where p is fixed). We would like to show that the hypergeometric approaches the binomial, i.e. im r=Np p fixed To show this, follow the instructions below in Excel: A1 A2 Name UIN Enter the following in the cells C1 to l1: p Binomial HyperGeometric Enter in cell: C2: the last two digit of your UIN D2: 1/3 of the cell 2. Round it to the closest whole number. E2 enter 0.6 F2: Calculate the binomial probability based on the values n, y and p. G2: enter 1000 12: Calculate the hypergeometric probability based on the values n, y, N and r. G3: G2 1000 Copy & paste cells G3:13 down. Does the hypergeometric approach the binomial?Explanation / Answer
THis shows that hypergeometric approach the binomial as N tends to infinity and p is fixed
n y p Binomial N r Hypergeometric 40 13 0.6 0.000283 1000 600 0.000223 40 13 0.6 0.000283 2000 1200 0.000252 40 13 0.6 0.000283 3000 1800 0.000262 40 13 0.6 0.000283 4000 2400 0.000267 40 13 0.6 0.000283 5000 3000 0.00027 40 13 0.6 0.000283 6000 3600 0.000273 40 13 0.6 0.000283 7000 4200 0.000274 40 13 0.6 0.000283 8000 4800 0.000275 40 13 0.6 0.000283 9000 5400 0.000276 40 13 0.6 0.000283 10000 6000 0.000277 40 13 0.6 0.000283 11000 6600 0.000277 40 13 0.6 0.000283 12000 7200 0.000278 40 13 0.6 0.000283 13000 7800 0.000278 40 13 0.6 0.000283 14000 8400 0.000279 40 13 0.6 0.000283 15000 9000 0.000279 40 13 0.6 0.000283 16000 9600 0.000279 40 13 0.6 0.000283 17000 10200 0.000279 40 13 0.6 0.000283 18000 10800 0.00028 40 13 0.6 0.000283 19000 11400 0.00028 40 13 0.6 0.000283 20000 12000 0.00028 40 13 0.6 0.000283 21000 12600 0.00028 40 13 0.6 0.000283 22000 13200 0.00028 40 13 0.6 0.000283 23000 13800 0.00028 40 13 0.6 0.000283 24000 14400 0.00028 40 13 0.6 0.000283 25000 15000 0.000281 40 13 0.6 0.000283 26000 15600 0.000281 40 13 0.6 0.000283 27000 16200 0.000281 40 13 0.6 0.000283 28000 16800 0.000281 40 13 0.6 0.000283 29000 17400 0.000281 40 13 0.6 0.000283 30000 18000 0.000281 40 13 0.6 0.000283 31000 18600 0.000281 40 13 0.6 0.000283 32000 19200 0.000281 40 13 0.6 0.000283 33000 19800 0.000281 40 13 0.6 0.000283 34000 20400 0.000281 40 13 0.6 0.000283 35000 21000 0.000281 40 13 0.6 0.000283 36000 21600 0.000281 40 13 0.6 0.000283 37000 22200 0.000281 40 13 0.6 0.000283 38000 22800 0.000281 40 13 0.6 0.000283 39000 23400 0.000281 40 13 0.6 0.000283 40000 24000 0.000282 40 13 0.6 0.000283 41000 24600 0.000282 40 13 0.6 0.000283 42000 25200 0.000282 40 13 0.6 0.000283 43000 25800 0.000282 40 13 0.6 0.000283 44000 26400 0.000282 40 13 0.6 0.000283 45000 27000 0.000282 40 13 0.6 0.000283 46000 27600 0.000282 40 13 0.6 0.000283 47000 28200 0.000282 40 13 0.6 0.000283 48000 28800 0.000282 40 13 0.6 0.000283 49000 29400 0.000282 40 13 0.6 0.000283 50000 30000 0.000282 40 13 0.6 0.000283 51000 30600 0.000282 40 13 0.6 0.000283 52000 31200 0.000282 40 13 0.6 0.000283 53000 31800 0.000282 40 13 0.6 0.000283 54000 32400 0.000282 40 13 0.6 0.000283 55000 33000 0.000282 40 13 0.6 0.000283 56000 33600 0.000282 40 13 0.6 0.000283 57000 34200 0.000282 40 13 0.6 0.000283 58000 34800 0.000282 40 13 0.6 0.000283 59000 35400 0.000282 40 13 0.6 0.000283 60000 36000 0.000282 40 13 0.6 0.000283 61000 36600 0.000282 40 13 0.6 0.000283 62000 37200 0.000282 40 13 0.6 0.000283 63000 37800 0.000282 40 13 0.6 0.000283 64000 38400 0.000282 40 13 0.6 0.000283 65000 39000 0.000282 40 13 0.6 0.000283 66000 39600 0.000282 40 13 0.6 0.000283 67000 40200 0.000282 40 13 0.6 0.000283 68000 40800 0.000282 40 13 0.6 0.000283 69000 41400 0.000282 40 13 0.6 0.000283 70000 42000 0.000282 40 13 0.6 0.000283 71000 42600 0.000282 40 13 0.6 0.000283 72000 43200 0.000282 40 13 0.6 0.000283 73000 43800 0.000282 40 13 0.6 0.000283 74000 44400 0.000282 40 13 0.6 0.000283 75000 45000 0.000282 40 13 0.6 0.000283 76000 45600 0.000282 40 13 0.6 0.000283 77000 46200 0.000282 40 13 0.6 0.000283 78000 46800 0.000282 40 13 0.6 0.000283 79000 47400 0.000282 40 13 0.6 0.000283 80000 48000 0.000282 40 13 0.6 0.000283 81000 48600 0.000282 40 13 0.6 0.000283 82000 49200 0.000282 40 13 0.6 0.000283 83000 49800 0.000282 40 13 0.6 0.000283 84000 50400 0.000282 40 13 0.6 0.000283 85000 51000 0.000282 40 13 0.6 0.000283 86000 51600 0.000282 40 13 0.6 0.000283 87000 52200 0.000282 40 13 0.6 0.000283 88000 52800 0.000282 40 13 0.6 0.000283 89000 53400 0.000282 40 13 0.6 0.000283 90000 54000 0.000282 40 13 0.6 0.000283 91000 54600 0.000282 40 13 0.6 0.000283 92000 55200 0.000282 40 13 0.6 0.000283 93000 55800 0.000282 40 13 0.6 0.000283 94000 56400 0.000282 40 13 0.6 0.000283 95000 57000 0.000282 40 13 0.6 0.000283 96000 57600 0.000282 40 13 0.6 0.000283 97000 58200 0.000282 40 13 0.6 0.000283 98000 58800 0.000282 40 13 0.6 0.000283 99000 59400 0.000282 40 13 0.6 0.000283 100000 60000 0.000282 40 13 0.6 0.000283 101000 60600 0.000282 40 13 0.6 0.000283 102000 61200 0.000282 40 13 0.6 0.000283 103000 61800 0.000282 40 13 0.6 0.000283 104000 62400 0.000282 40 13 0.6 0.000283 105000 63000 0.000283