Probability question in telephone network failures

[twoflower]

Hi,

I have this problem

Homework Statement

In telephone network, an average number of failures during a month for one telephone owner is 8. What is the probability that some telephone owner will experience more than 4 failures?

The Attempt at a Solution

I have no idea what distribution should I use to model this problem. So far I've come up with binomial distribution with probability of individual event 8/k, where k is number of connection the telephonist will make during a month.

But that seems really odd to me...

Could someone help please?

Thank you.

 

[AlephZero]

So you have the situation where there are k trials (attempted calls), the probability of "success" (i.e. there is a fault) is 8/k, and k is probably large.

What distribution is an approximation to the Binomial(n,p) as n becomes large and np stays constant?

 

[twoflower]

So you have the situation where there are k trials (attempted calls), the probability of "success" (i.e. there is a fault) is 8/k, and k is probably large.

What distribution is an approximation to the Binomial(n,p) as n becomes large and np stays constant?

One way is to approximate it with Poisson distribution, but can I solve it using Central Limit Theorem? Which one is better?

 

[twoflower]

I tried to finish it using the Poisson distribution and it seems ok.

Anyway, using Central Limit Theorem I got result depending on n, is it ok?

 

[lkh1986]

Yeap, I think Poisson distribution is more appropriate here.