# Thread: A coil of wire has 400 metres of wire. Suppose there are 20 nicks.

1. ## A coil of wire has 400 metres of wire. Suppose there are 20 nicks.

A coil of wire has 400 metres of wire. Suppose there are 20 nicks (the most common problem with wire) are randomly distributed on a coil.

What is the probability that in a 40 metre length of wire there will be at least 6 nicks?
What is the probability that in a 49 metre length of wire there will be exactly 4 nick(s)?

I know that I have to use the poisson distribution, but I have to do it in excel using
=POISSON(x,mean,1 or 0), and I have no idea what to do.

2. If you know there are exactly 20 nicks in the 400 metre coil, then the poisson distribution may be inappropriate. This is because the poisson distribution will give a nonzero probability of finding more than 20 nicks in any segment.

however if your teacher told you to use the poisson distribution then I would assume that the expected number of nicks per metre is 0.05. (20/400 =0.05).

The number of nicks (x) in a segment of length (k) is then distributed as $\sim Po(0.05k)$

(a)The number of nicks on a segment of length 40 follows a po(0.05*40) = po(2) distribution

$P(x \geq 6) = 1-p(x \leq 5)$

Excel will tell you $p(x \leq 5)$:
in excel 2003, this is POISSON(5,2,1)