# Can I use a Poisson distribution for non-normal binomial data?

#### alex242

##### New Member
Hello all. I'm working on the following question:

Fifteen percent of the items produced by a machine are defective. Out of 15 items chosen at random,
a)what is the probability that exactly 3 items will be non-defective?

Now this is a binomial distribution but; pn = 85/100 (15) = 12.75 and qn = 15/100 (15) = 2.25 (right?)
With qn being so low this isn't suitable for normal approximation and so the binomial distribution can't work here right? (I tried calculating it and realized z scores seemed much too high)

So can I use the Poisson distribution for this problem? And if I do, do I have to calculate upper and lower limits (3.5 & 2.5 respectively) and then subtract one from the other like I would for the binomial distribution, or will I just use one X value of 3 for the equation?
I haven't been able to find much help online about using the Poisson distribution for just two outcomes.

Let me know if I'm missing something here.
Really appreciate any help or advice!