Thread: Probability - Poisson

Suppose that the number of chocolate chips in a cookie follows the poisson random variable with lambda=4.

What is the probability that a package of 9 cookies will have exactly 36 chips?

So I know that lambda is the mean so each cookie should have 4 chips on it which seems to correspond with the factg that 36/9 = 4 also.

Does the mean change when you have more cookies?

How would you set this problem up. I assume it will have something to do with:
Pr = e^(neg lambda) * (lambda^y)/(y!)

Thanks in advance.

Originally Posted by DINOCALC09

Suppose that the number of chocolate chips in a cookie follows the poisson random variable with lambda=4.

What is the probability that a package of 9 cookies will have exactly 36 chips?

So I know that lambda is the mean so each cookie should have 4 chips on it which seems to correspond with the factg that 36/9 = 4 also.

Does the mean change when you have more cookies?

How would you set this problem up. I assume it will have something to do with:
Pr = e^(neg lambda) * (lambda^y)/(y!)

Thanks in advance.

Let X be the random variable "number of chips in packet of 9 cookies". Use Poisson with mean = (4)(9) = 36 and calculate Pr(X = 36).

Pr(X=36) = e^(-36) * [(36^36)/(36!)] = approx 0.0663 ???

Since new lambda = 36 as a result of multiplying 4*9, that would mean a poisson model is probably not the best approximation since nm > 5, correct? Or am i misunderstanding something.