Trying to confront a company regarding defective rates for units.

Question

I have tried to do this myself, but the math escapes me *sigh*

I am a forum owner and a company is having serious defective issues. We know that their "claimed" defective rate is WAY off and we are attempting to prove it mathematically.  Here is the relevant information.

 

They claim a 3% to 5% defective rate. Assume 1,000,000 units and I need the chance of receiving 1, 2, 3 and 4 units in a row based on their claimed defective rate. Preferable the % chance for each, between 1 and 4 defective units in a row. If someone knows the equation and answer for this problem, you're my hero! lol

Answer 1

I wouldn't worry about the number of defectives in a row. In a million consecutive units, you should not have 50,000 defectives at any point. In a 1,000 consecutive units, you should not have more than 50 defectives. And in 100 consecutive units, you should not have more than 5.

Without more information about the standard deviation, you would really need a million consecutive units. But in any smaller sample in which the 5% rate was exceeded, it would veca good bet that the 5% was false.