Misprints are distributed randomly and uniformly in a book at a rate of 2 per 100 lines. What is the probability that a line is free of misprints?

Question

kirbykirby · Answer

I thought this was simply saying that 2 lines of 100 have errors
So, there are 100-2=98 lines out of 100 that are error free (on avg. )

So, Probability = 98/100 = 0.98

But, my book uses a Poisson distribution: Let X be the # of errors

μ=λt where λ = 0.02/line, t = 1 line, so μ=0.02

$$P(X=0)=\frac{(0.02)^0e^{−0.02}}{0!}$$
=0.9802 (which is still close to 0.98... but I wonder why we need the Poisson here?)

amistre64 · Answer

randomly and uniformily, so its not a normal distribution

amistre64 · Answer

Poison does seem most applicable

amistre64 · Answer

the simplicity might be so that you can reasonably determine the correctness of the poison method for this

kirbykirby · Answer

Hm. So you can use the Poisson for  things that don't involve periods of time (which is what we usually saw)?

amistre64 · Answer

correct.  most likely this problem can relate very well to a time based setup

kirbykirby · Answer

oh ok interesting. thanks :)