# Poisson distribution

• Nov 4th 2010, 12:50 AM
CautionItsHot
Poisson distribution
A manufacturer of rockets estimates that on average 1 in 75 of the rockets fail to burn properly.Using this estimate, and a Poisson distribution, find an approximate value for the probability that out of 225 randomly chosen rockets at most 221 burn properly.

How do i solve this question using poisson distribution? I solve this question using binomial dist, using X~B(225,74/75) P(Xless than or =221). But the question says use poisson?How do i do it the poisson way?
• Nov 4th 2010, 02:14 AM
Quote:

Originally Posted by CautionItsHot
A manufacturer of rockets estimates that on average 1 in 75 of the rockets fail to burn properly.Using this estimate, and a Poisson distribution, find an approximate value for the probability that out of 225 randomly chosen rockets at most 221 burn properly.

How do i solve this question using poisson distribution? I solve this question using binomial dist, using X~B(225,74/75) P(Xless than or =221). But the question says use poisson?How do i do it the poisson way?

Edit:

We will need to adjust the mean first. If there is 1 defective rocket in 75 rockets, there will be 3 defective rockets in 225 rockets. Also, it's the same as calculating the probability of at least 4 rockets did not properly burn, P(x>=4) with the poisson mean of 3.
• Nov 4th 2010, 05:34 AM
CautionItsHot
I dun think your method, which is 1-P(X<=3) using 1/75 as the mean , will get the correct ans which is 0.353. Am i wrong?
• Nov 4th 2010, 06:03 AM