Variation of the coupon problem

[Smitz]

I have a problem which is basically a variation of the coupon problem... I can't get my head around it as I haven't done much stats .

I have a sample size of 900, say a pot of 900 balls, each with a unique id. Each week I am going to select a set number of balls randomly from the pot to test them. After testing, the balls go back into the pot. How many balls do I need to test every week so that after 3 years I can be, say, 90% confident that 90% of the sample have been tested in that period.

Any help would be greatly appreciated (especially a solution!)

Andrew

 

[EnumaElish]

This is related to the critical sample size problem:
http://en.wikipedia.org/wiki/Confidence_interval

E.g. to apply a "two-tailed" test to a given value x of a normally distributed random variable with mean m and variance σ², one can define z = (x - m) / (σ/√n) then solve Φ(z) = 0.975 for n, where Φ is the cumulative normal distribution function.