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Poisson distribution homework

  1. Apr 16, 2014 #1
    1. The problem statement, all variables and given/known data

    A rectangular field is gridded into squares of side 1m. at one time of the year the number of snails in the field can be modelled by a Poisson distribution with mean 2.25 per m^2.
    (i) a random sample of 120 squares is observed and the number of snails in each square counted. find the probability that the sample mean number of snails is at most 2.5

    2. Relevant equations
    using central limit theorem, sample mean of X ~N (2.25, 2.25x1/120=0.01875)

    p(sample mean of x<=2.5)
    =p(z<(2.5+1/240-2.25)/ √0.01875)
    =p(z<1.856)
    =09682


    3. The attempt at a solution
    Is this correct? any1? becuz im nt sure whether poisson can do this way onot in sampling
     
  2. jcsd
  3. Apr 16, 2014 #2

    Ray Vickson

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    Please write proper english here; any1 = anyone, im = I'm, etc, etc. After you fix that up I will be glad to tell you whether or not I agree with your solution.
     
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