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I'm trying to understand whether I can use the binomial distribution in a certain way...

According to the equation, to find the probability P of a certain number of successes out of a number you trials, you need the number of trials, n; the number of successes out of the trials, x; and the probability of a success on any given trial, p.

Now let's say you have a small population size, N = 40, of LEDs, that either work or don't. Can I assume p to be .50 and and set P to .95 so I can determine what n and x I would need? Or am I supposed to do a preliminary study to determine p?

Are there other tests I should do instead for finding the probability of failure in small population and small sample sizes? Is there a minimum % of the population that I should test?

I haven't found any problem like this in any of the textbooks I've looked through.

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# Binomial Probability Problem

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