Bacteria Colony Distribution in a Nutrient Dish

[Redhead711]

Hello, I have been stuck on this problem for about a week and a half. I was wondering if there was anyone out there who might understand it and explain it clearly to me.

Suppose a volume of 1000 drops of water contains 2000 bacteria, separate from each other and thoroughly mixed in the water. A single drop is smeared uniformly over the surface of the dish. The dish contains nutrients on which the bacteria feed and multiply. After a few days, wherever a bacterium was deposited on the dish a visible colony of bacteria appears. Find the distribution of the number of colonies that appear. (a) over the whole plate, and (b) over an area of half the plate.

 

[BicycleTree]

You should use the Poisson distribution. You know what the mean should be?

Or to be exact, you could use the binomial distribution where each success is finding a particular bacterium of the 2000 in the drop, so n = 2000 and you can figure out p. But the Poisson should be very accurate.

 

[Redhead711]

Thank you very much for your help