A process produces faulty items with probability 0.04. Samples of 100 items are taken from batches at random and if there are less than 5 faulty items in the sample then the batch is accepted; otherwise the batch is rejected.
I have attempted to calculate the probability that a batch is rejected by summing the binomial probabilities for r=0,1,2,3,4.
I obtain the answer 0.6289 but would appreciate confirmation that I have used the correct approach and done the calculation accurately.
You set the Parameters for binomial Distribution $p = 0.04, N = 100$. $X$: number of faulty items.
The probability for rejection is $P (X > 5) = \sum_{k=6}^N (n|k)p^k(1-p)^{n-k}$ since for $k>5$ the Batch is rejected.