Poisson Distribution Questions and Answers

Under which conditions can the Poisson distribution be used as an approximation to the Binomial distribution?

Potato seeds are packed in packets of 200 seeds, with on average 2% of the seeds in a packet rotten. A packet is substandard if it contains 5 or more rotten seeds. Using a Poisson approximation with mean $\lambda=200\times0.02=4$, what is the probability that a packet is substandard, correct to 3 decimal places?

A random sample of 100 observations from a population gave $\sum(x - 50) = 123.5$. What is the unbiased estimate of the population mean $\mu$, to 3 decimal places?

A company receives on average 6 orders per day, following a Poisson distribution. What is the probability that no more than 2 orders will be received on a given day, to 3 decimal places?

Weekly supply to car dealer B follows a Poisson distribution with mean $\frac{2}{3}$ cars. What is the probability that, in a given week, fewer than three cars are supplied to B?

Weekly supply to car dealer A follows a Poisson distribution with mean $\frac{4}{3}$ cars, and weekly supply to car dealer B independently follows a Poisson distribution with mean $\frac{2}{3}$ cars. What is the probability that, in a given week, fewer than three cars in total are supplied to A and B combined?

In a particular survey involving 7076 households, 0.0248% were in favour of amending city council by-laws. The number in favour is to be modelled by a Poisson approximation to the binomial.