Suppose that, on average, a bushel of 100 apples contain three apples with a worm. Select a bushel of 100 apples at random. Let $Worm$ be the random variable that represents the number of apples with a worm. Assume that the number of apples that contain a worm can be modeled by a binomial random variable with parameters n=100, and p=0.03. Find $\Pr(Worm=k)$ for $k=0,1,2,3,4,8$. Compare these with the Poisson model.
For the binomial model, I know that the equation is as follows:
I was having a little trouble developing the equation with the Poisson model, specifically the lambda parameter. I understand that lambda is the rate of occurrence. For example, we might know that there are 500 misprints in a 250 page manuscript, which translates into an average rate of $\lambda=500/250=2$ misprints per page.
In this problem, I thought $\lambda=3/100$ giving the following equation:
but apparently $\lambda = 3 $. Can someone please explain why? I thought lambda is a rate so it should be 3 rotten apples per a bushel of 100 apples, not (3/100)*100 = 3....