It is found that 5% of screws in a factory are found to be defective. Use the Poisson theorum and the binomial theorum to compute the probability that two or more are found to be defective if a sample of 20 screws is tested.
Can anyone pleasssssse help me with this I've been at it for ages, I'm ok at the binomial but hard to know what to put into formula but really dnt get the Poisson theorum??? Thanks so much :)
How to start binomial?
The approximation here is $$ B(n,p)\simeq Poisson (np). $$ where the Poisson distribution is such as $$ P(N=k) = \exp(-np)\frac{(np)^k}{k!} $$ ($\exp$ is the exponential).
Here $n=20, p = 0.05$ so $np=1$.
Then with $N$ being the number of defective screws: $$ P(N\ge 2) = 1 - P(N=0) - P(N=1) \simeq 1- \frac{\exp (-1)}{0!} - \frac{\exp (-1)}{1!} \simeq 0.26 $$