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Poisson Distribution problem in stats?
The distribution of dandelions in a large meadow is approximately Poisson, with a mean of 4 dandelions per square meter. For a randomly selected one meter plot in this meadow:
1) What is the probability there are more than 2 dandelions?
2) Given there is at least one dandelion, what is the probability there are exactly three?
3) What is the standard deviation of the number of dandelions in a square meter?
I know how to find standard deviation, mean, probability etc. I just have no clue how to go about solving these questions. Could someone help me out? point me in the right direction?
Thanks in advanced.
1 Answer
- PaulaLv 71 decade agoFavorite Answer
Nearly all your answers come from the poisson distribution formula:
P(n=k) = e^-L L^k / k!
Where L (usually written as the greek letter lambda) is the mean; and in the case of a poisson distribution, the variance is equal to the mean. So in this case, L=4.
e.g. for the probability of 0 dandelions per square metre (P(n=0)), put k=0 and L=4 into the equation above.
(a) P(at least 2 dandelions) = P(n>=2) = 1 - P(n=0) - P(n=1)
(b) P(3 given there are at least 1) = P(n=3) / P(n>=1) = P(n=3) / (1 - P(n=0))
(c) square root of the variance
