1. ## Binomial/Poisson/Normal

You are a judge of quality and over time you conclude that 10% of all videos on facebook are hilarious. A friend suggests a facebook marathon of 100 videos as way to kill time.

(a) For each of the Binomial, Poisson and Normal distributions, write down a formula

This is what I did for binomial:

Then for the normal distribution I did the binomial/normal approximation:

However using my calculator the value I get from the binomial is P(3<=X<=7) = 0.2041

But from the normal approximation I get P(3<=Y<=7) = 0.1488

The value from the normal approximation is a bit low... so I thought I might have done something wrong, is it because the approximation can only work if p is not too close to 0 or 1? And since p = 0.1 it is fairly close to 0...

Any help would be appreciated, thanks

2. That's exactly why you need the correction factor.

$\displaystyle P(3\le Bin\le 7)\approx P(2.5<Normal<7.5)=P\left({2.5-10\over 3}<Z<{7.5-10\over 3}\right)$

3. What about the Poisson approximation?

$\displaystyle e^{-10}\sum_{k=3}^7 {10^k\over k!}$

4. Yeah the poisson was alright the approximation was ~ 0.2175

However I haven't learnt this "correction factor", what is it exactly?

5. Originally Posted by usagi_killer
Yeah the poisson was alright the approximation was ~ 0.2175

However I haven't learnt this "correction factor", what is it exactly?