# In a Poisson distruibution mu=4...

• March 24th 2008, 05:26 AM
aawb9c
In a Poisson distruibution mu=4...
Hi lifesavers! I need some assistance. I need a formula so I can solve the following:

In a Poisson distribution where mu=4:

a)What is the probability x=2?

b)What is the probability x is less than or equal to 2?

c)What is the probability x is greater than 2?

THANK YOU SO VERY MUCH! I appreciate your help tremendously!
• March 24th 2008, 05:47 AM
mathceleb
Quote:

Originally Posted by aawb9c
Hi lifesavers! I need some assistance. I need a formula so I can solve the following:

In a Poisson distribution where mu=4:

a)What is the probability x=2?

b)What is the probability x is less than or equal to 2?

c)What is the probability x is greater than 2?

THANK YOU SO VERY MUCH! I appreciate your help tremendously!

Poisson Distribution

We know that lambda is the mean, so we need it to equal 4. Enter 10 for n, 0.4 for p, and 2 for k and press enter: Take a look at the entire math work and the answer and let me know if you have questions.

For b, P(x<=2) = P(x=0) + P(x=1) + P(x=2). 0.018 + 0.073 + 0.147 = 0.238. You can use my calculator if you want, or try to do what you did above for question (a) 2 more times for x = 0 and x = 1. Take a look at the formulas on my page and let me know if you have questions.

For c, we know that P(x > 2) = 1 - P(x<=2). So, essentially, it's 1 - your answer for (b). 1 - .238 = 0.762.

Later tonight I'll have the function built on the calculator to calculate cumulative probabilities for questions b and c automatically. I'll PM you or notify you on this thread when that is ready. It will show you the math for each success mentioned above, i.e., P(x=0) + P(x=1) + P(x=2). For now though, try it manually.
• March 24th 2008, 05:59 AM
aawb9c
Me again. I was wondering how you calculated that n=10 and p=.4. Also, my options for all three parts are:

a)0.7619
b)0.1465
c)0.2381
d)0.2456

Those are all different from the answers you gave me. This stuff is so confusing to me!!!!
• March 24th 2008, 06:00 AM
aawb9c
Nevermind....
I'm a complte idiot, you just rounded. So forget that multiple choice thing!! Thanks. But could you still tell me how you got what the p and n equaled? THANK YOU!!!!!!!!!!!!!!!!!!!
• March 24th 2008, 06:07 AM
mathceleb
Quote:

Originally Posted by aawb9c
I'm a complte idiot, you just rounded. So forget that multiple choice thing!! Thanks. But could you still tell me how you got what the p and n equaled? THANK YOU!!!!!!!!!!!!!!!!!!!

Sorry, my calculator rounds to 3 digits, I'm going to change that to 4 tonight by request.

Now, as for the question about n and p, you can disregard using n and p in the problem you are given. The mean of a Poisson distribution is n*p. My Calculator doesn't have it built in yet to just enter mean, so I gave you 2 "filler" values which I knew the product of would equal your mean of 4. You don't need to find "n" and "p" in the problems that you asked, I just gave it to you so that you could use my calculator and see the entire math work needed to get to the answers.

I also did it for another reason though. In future Poisson problems, you may not be given the mean served up on a platter. I wanted to show you what the mean represents.

For example, if a problem is given that states, "Using a Poisson distribution, the probability of a person passing an obstacle course is 0.4. Calculate the probability of them passing the course exactly 2 times in 10 tries. The mean in this case would be n * p = 10 * 0.4 = 4.

For your problem though, if you look at the math on my site, you had everything you need up front to calculate since $\mu = \lambda$ which is the mean.

Does all that make sense?
• March 24th 2008, 06:52 AM
aawb9c
Yes!!
Yeah, it is all coming together for me now! Thanks a TON!! I am all smiles now. And that calculator will come in handy in the future. You're awesome!(Yes)
• March 24th 2008, 04:44 PM
mathceleb
Quote:

Originally Posted by mathceleb
Later tonight I'll have the function built on the calculator to calculate cumulative probabilities for questions b and c automatically. I'll PM you or notify you on this thread when that is ready. It will show you the math for each success mentioned above, i.e., P(x=0) + P(x=1) + P(x=2). For now though, try it manually.

I PM'ed you as well. As promised, question b and question c are now automated. You may need to refresh your browser to see the changes. You should see 3 buttons now. Go here again:

Poisson Distribution

For question a, the button that says "exactly k successes" was question a that you asked. That worked as we know before, it just has a diferent label now.

For question b, you would now enter the same information you did before, and press the second button that says "no more than k successes".

For question c, you would now enter the same information you did before, and press the third button that says "greater than k successes".

For question b and c, you see we match our answers that we discussed this morning. Scroll down as there are many more lines of math to go through. Basically, it calculates each probability for each k up to the k amount you specify. Then it takes a cumulative probability measure like we talked about.

As also promised, I round all probabilities to 4 digits now instead of 3. Have a good evening.
• March 24th 2008, 05:15 PM
aawb9c
Thank You Thank You Thank You!
I am seriously ecstatic right now. You have no idea how much you have helped me! I cannot say enough how great it is that you spent the time customizing that calculator for me and replying to my questions! You are amazing and I thank you from the bottom of my heart!!

Ashley