- #1

sunrah

- 199

- 22

## Homework Statement

A teacher has an infinite flow of papers to mark. They appear in his office at random times, at an average rate of 10 a day. On average 10% of the manuscripts are free from errors. What is the probability that the teacher will see exactly one error-free manuscript (a) after he has marked 10 of them? (b) after a day?

## Homework Equations

Binomial dist.:

[itex]P(k) = \frac{N!}{k!(N-k)!}p^{k}(1-p)^{N-k}[/itex]

Poisson dist.:

[itex]P(k) = \frac{\mu^{k}}{k!}e^{-\mu}[/itex]

## The Attempt at a Solution

a)

The first part seemed straight forward, just plug on following values

No. of trials: N = 10

No. of successes: k = 1

Prob. of success: p = 0.1

This gives an answer ~0.4 (1 s.f.)

b) The second part I don't really understand. I know it goes to a Poisson distribution because I asked my teacher if that is so. I thought P-distributions are for very large N? Can we assume that here? Mean I know the no. of papers i infinite, but the per day average is only 10?

Secondly is the mean value per day μ, the same as the expectation value per 10 papers? I don't think so, but here goes:

let μ = 0.1 and using second equation -> P(1) = ~0.2 (1 s.f)

I thought given the same parameters, the Poisson and Binomial distributions should give very similar results.