Question goes as follows:
It is known that $0.15$ of products sold by store are defected in some way and have to be replaced. The shop has $1200$ products in storage. What is the probability that an order of $1000$ and the replaced products of that order (because of defects) can be made (I assume with the 1200 products in storage).
My reasoning goes as follows. Since we sell $1000$ products from the storage, we have to figure out what is the probability that the number of defected products is less or equal to $200$. I think this follows Binomial distribution but since $min:(np,np(1-p))>5$ I tried to arpoximate it with normal distribution;$$Mean = .15*1000=150$$ $$Var=1000*.15*.85=127.5$$ $$N(150,127.5)$$ X = number of products defected
$$P(X\le200)=\phi(\frac{200.5-150}{\sqrt{127.5}})=\phi(4.472)\approx0.999996$$
This answer for me feels too certan. The $4.4$ siqma event isn't even on the spreadsheet I am using (had to use excel).
So my question is can some one check if I am right and if not give me some hint what to do differently?