Probability of Sample Mean for Poisson Distribution

[Unusualskill]

Homework Statement

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 modeled 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

Homework 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

The Attempt at a Solution

Is this correct? any1? becuz I am nt sure whether poisson can do this way onot in sampling

 

[Ray Vickson]

Homework Statement

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 modeled 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

Homework 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

The Attempt at a Solution

Is this correct? any1? becuz I am nt sure whether poisson can do this way onot in sampling

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