# Probability Question About The Poisson Probability Distribution

Probability Question About "The Poisson Probability Distribution"

## Homework Statement

- Assume that 1 in 200 people carry the defective gene that causes inherited colon cancer. A sample of 1000 individuals is taken.

Use the Poisson approximation to calculate the appoximate standard deviation of the number of people who carry the gene.

## The Attempt at a Solution

I am honestly having a hard time even getting started with this one. I think I find Lamda by setting 1-$$e^{-\lambda1000}$$=1/2

Dick
Homework Helper

What does it say lambda is in the definition of a Poisson distribution?

It says that Lamda is "frequently a rate per unit time or per unit area".

Dick
Homework Helper

That's not helpful. You could describe a lot of things that way. Nothing more specific? Check wikipedia if your reference is completely lame.

It also says that lamda is equal to n*p. I think I need to use the entire population (1000) for n. But I have no idea what to use for 'p'.

Dick
Homework Helper

It also says that lamda is equal to n*p. I think I need to use the entire population (1000) for n. But I have no idea what to use for 'p'.

Maybe 'p' has something to do with '1 in 200'.

According to Wikipedia: "λ is a positive real number, equal to the expected number of occurrences that occur during the given interval. For instance, if the events occur on average 4 times per minute, and you are interested in the number of events occurring in a 10 minute interval, you would use as your model a Poisson distribution with λ = 10×4 = 40".

So it looks like lamda = 1000*1/200 = 5 (if I'm understanding this)

Dick
Homework Helper

According to Wikipedia: "λ is a positive real number, equal to the expected number of occurrences that occur during the given interval. For instance, if the events occur on average 4 times per minute, and you are interested in the number of events occurring in a 10 minute interval, you would use as your model a Poisson distribution with λ = 10×4 = 40".

So it looks like lamda = 1000*1/200 = 5 (if I'm understanding this)

You are understanding correctly.

Okay, cool. That gets me started then. I'll see what I can drum up here. Thanks for your help.

So it looks likeE(X) = V(X) = Lamda. So finding the standard deviation should be as simple as finding the square root of five right?

Dick
Homework Helper

So it looks likeE(X) = V(X) = Lamda. So finding the standard deviation should be as simple as finding the square root of five right?

Yes, it's that simple. Do you know why it's only the 'approximate' standard deviation for a sample of 1000?

I'm assuming it is because the square root of five is an irrational number.

Gotta get to class. Thanks for helping me. I appreciate it.

Dick
Homework Helper

I'm assuming it is because the square root of five is an irrational number.

No, it's because a Poisson distribution only 'approximates' a binomial distribution with a large sample size. For a binomial distribution V(X)=n*p*(1-p), but since 1-p is almost 1, you get almost the same thing. That's why they said 'approximate'. Just so you know.

No, it's because a Poisson distribution only 'approximates' a binomial distribution with a large sample size. For a binomial distribution V(X)=n*p*(1-p), but since 1-p is almost 1, you get almost the same thing. That's why they said 'approximate'. Just so you know.

Okay, got it. My teacher is just terrible. You have helped me more about this than pouring over this book, and every lecture that guy could ever give. Thanks again.

Dick