## Poisson Approximation to Binomial Exercise

1. X is a random variable with a binomial distribution with n = 200 and p = 0.04.

a. Use the binomial probability formula to find P(X = 0) and P(X = 2)

b. Use the Poisson distribution to find P(X = 0) and P(X = 2).
Was is appropriate to use the Poisson as an approximation in this case?

2. On average one person in 200 has a serious accident at work in a given year. What is the probability that in a sample of 920 people five people will have an accident.

 3. A 747 plane has 360 seats. An airline has found that on average 1% of people with tickets do not turn up. Find the probability that more than 4 people do not turn up for a flight. 4. A factory produces a large number of appliances, which are supposed to meet given specifications. A proportion, π, of the appliances are faulty because they do not meet these specifications.
A random sample of n appliances is taken, and each appliance is inspected. Let the random variable X be the number of faulty appliances in the sample.

Suppose that n =10 and π = 0.02

a. What distribution will approximate the distribution of X? (Give the name of the distribution and its parameter(s). Justify your choice of distribution.

b. Use this approximation to find the probability that the sample contains fewer than two faulty appliances.