# Poisson distribution and binomial distribution questions

1.
(a) Define the Poisson probability distribution with mean μ.

(b) Write down the binomial distribution for x successes in n independent trials each with probability p of success.

(c) On average, 0.15% of the nails manufactured at a factory are known to be defective. If a random sample of 400 nails is inspected, what is the probability of there being no more than 3 defective nails?

4.
(a) Define the Poisson probability distribution with mean p.

(b) A tool hire shop has six lawn mowers which it hires out on a daily basis.The number of lawn mowers requested per day follows a Poisson probability distribution with mean 4.5. Find the probability that:

(i) exactly three lawn mowers are hired out on any one day;
(ii) all lawn mowers are in use on any one day.