Answer to Question #146695 in Statistics and Probability for fahmi

Question

When pond water is examined under the microscope there are nasty bugs to be seen. The average concentration of these bugs is 3 per milliliter. Determine the probability that a random sample of 5 milliliters of pond water contains exactly 14 bugs:
a) Using the Poisson distribution.
b) Using the Normal approximate to the Poisson distribution.

Answer 1

The provided mean is 

$\lambda= 3$

a)We need to compute Pr(X=5). Therefore, the following is obtained using ti84,Pr(X=5)=0.10082

b)Using the Normal approximate to the Poisson distribution.

mean = $n*\lambda$ =5*3=15

sd= $\sqrt{(n*\lambda)}$ =$\sqrt{15}=$ 3.873

Hence P(x=14)= =NORMSDIST((14.5-15)/SQRT(15))-NORMSDIST((13.5-15)/SQRT(15))=0.099372