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