- #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.