Q: if 15 out of 100 products failed quality control (15% failure rate) how many products out of the next 100 need to be randomly selected to be fixed to be 95% sure that the failure rate has been brought down to 2% post-quality control?

Question

Thanks for your help, my quant guy at work is blowing me off an I haven’t done math since high school.

Answer 1

If the error rate is the same, you need to catch 13 of the errors. That leaves two errors, or 2/100=2%. With an error rate of three out of any 20, you would need to check 86.666 out of 100 to average a 2% remaining error rate. Formula would be 100-100*2/15.

Answer 2

Sounds like a high fail rate.

Answer 3

I presume you mean "down to no more than 2%".