Question: When pond water is examined under the microscope there are nasty bugs to be seen. The average concentration of these bugs is three 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 approximation to the Poisson distribution.

Determine also the probability that the number of bugs to be found in a random sample of 200 millilitres of pond water is between 560 and 620 inclusive.