Poisson distribution question

[semidevil]

ok, so on average, there is a chromosome mutation link once every 10,000 baby births.

approximate the probability that exactly 3 of the next 20,000 babies born will have the mutation.

so using poisson distribution, I let
p = 1/10,000
n = 20,000.

and use formula (e^(-np) * (np)^k / k!

so when I do the calculation, do I sum it all up for k = 1, 2, 3, or do I just calculate k = 3 and that is my final answer?

if they ask at most 3, then I would sum up k = 1, 2, 3 right?

I first applied the formula for k = 1, 2, 3, but then it got me thinking about it...

 

[wais]

Your approach is correct. You would use the Poisson distribution formula to calculate the probability of exactly 3 babies out of 20,000 having the mutation. This would involve calculating the probability for k = 3 only.

If the question asked for at most 3 babies, then you would need to sum up the probabilities for k = 1, 2, and 3. This would give you the probability of 3 or fewer babies having the mutation.

It is important to carefully read and understand the question to determine which approach to use. In this case, the question specifically asks for the probability of exactly 3 babies having the mutation, so you would only need to calculate for k = 3.