[Math] Poisson Distribution – dealing with big numbers

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The mean number of defective products produced in a factory in one day is 21.
What is the probability that in a given day there are exactly 12 defective products?

I get some big numbers when I try to answer this question and they don't make sense !

I used a Poisson Distribution calculator to get the answer
0.0116

But when I use my calculator to figure it out I get
1.0917004899798243054141947918587e-13

Where am I going wrong?

I use the basic formula for Poisson Distribution

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The mean is 21

and X is 12

Best Answer

Poisson is used when n tends to infinite and the probability tends to zero. In my opinion you should try using Binomial Distribution.

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