# Math Help - Help with Poisson distribution

1. ## Help with Poisson distribution

i have a question, if possible, I need some one to help me to solve it. I know it's easy but it kind make me dizzy.

if a cable is manufactured with probability of 0.001 that has one blemish per foot and probability of 0 for more than a blemish with same length. If X is the number of blemish per 3000 feet, get the Pr(X=5) ??

is the solution will be as follow:

mu = n * p = 3000 * .001 = 3

Pr(X=5) = [ 3^5 * e^(-3) ] / 5! = .100 =10% (Poisson Distribution)

2. Originally Posted by ktoobi
i have a question, if possible, I need some one to help me to solve it. I know it's easy but it kind make me dizzy.

if a cable is manufactured with probability of 0.001 that has one blemish per foot and probability of 0 for more than a blemish with same length. If X is the number of blemish per 3000 feet, get the Pr(X=5) ??

is the solution will be as follow:

mu = n * p = 3000 * .001 = 3

Pr(X=5) = [ 3^5 * e^(-3) ] / 5! = .100 =10% (Poisson Distribution)
Yes that seems correct. Using my tables I get $P(X \leq 5) = 0.9161$ and $P(X \leq 4) = 0.8153$, therefore $P(x = 5) = P(X \leq 5) - P(X \leq 4) = 0.1008$.

3. thanx man; you are quick

can you just explain your answers plz. and which table did u used?

4. Originally Posted by craig
$P(x = 5) = P(X \leq 5) - P(X \leq 4) = 0.1008$.
Poisson is a discrete distribution, therefore the values can only be integers, 1,2,3 etc. $P(X \leq 5)$ are the values from 0..5. $P(X \leq 4)$ are the values 0..4.

This implies that $P(x = 5) = P(X \leq 5) - P(X \leq 4)$.

The tables that I use are Poisson statistical tables. They are basically a shortcut for working out probabilities without doing the calculations. If your course does not use them though, then I do not recommend using them, as this could have a negative affect when you come to do the calculations the the exams and you've not a clue how to do them

From what I've seen though you seem to have got to grips with the distribution quite fine.

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