 #1
Seneka
 41
 0
 Homework Statement:
 The number of mistakes a teacher makes while marking homework has a poisson distribution with mean of 1.6 errors per piece of homework. Find the probability that in a class of 12 pupils fewer than half of them have errors in their marking.
 Relevant Equations:

P(X=r)= (e to the power  lambda)(lamba to the power r) all divided by r factorials
where lamba is the average rate of the event.
the expected and variance are both equal to the average rate of the event.
Mentor edit: ##P(X = r) = e^{\lambda}\frac{\lambda^r}{r!}##
LaTeX script: # #P(X = r) = e^{\lambda}\frac{\lambda^r}{r!}# #
So I thought you would find the probability of having 0 errors when the mean rate is 1.6. Square that by 5 and multiply that by one minus the probability of having 0 errors to the power of 7. So that is basically the probability of having 0 errors to the power of 5 multiplied by the probability of having one or more errors to the power of 7 for the 7 students that do get errors in their marking. This gave me 6.919...x10 to the power 5 which is not the answer.
The answer is 0.00413.
The answer is 0.00413.