Re: Statistics
I wasn't taught the hypergeometric distribution properly so can someone walk me through how to use it? Here's my question if it helps to refer to it.
A factory produces 80 items in a batch. To test if the batch is defective, an acceptance sampling scheme is adopted: a random sample of 10 items is selected, and if 2 or more items don’t meet customer specifications, the batch is considered defective.
If there are actually 11 defective items in the batch,
1i) What is the probability that 2 sampled items are defective?
ii) What is a general formula for x sampled items being defective?
 \ge 0\text{ or }\mathbb{P}(A) > 0?)
 = \frac{{\binom K k } {\binom {N-K} {n-k}}}{\binom N n} \\ \\$Here N = 80, K = 11, n = 10 and for (i) k = 2$ \\ \\ $ So: $ P(X = 2) = \frac {\binom {11} 2 \binom {80-11}{10-2} }{\binom {80} {10}} \\ \\ $ For k = x: $ P(X = x) = \frac {\binom {11} x \binom {80 - 11} {10-x}}{\binom {80} {10}})
