6 The number of house sales per week handled by an estate agent is modelled by the distribution \(\operatorname { Po } ( 3 )\).
- Find the probability that, in one randomly chosen week, the number of sales handled is
(a) greater than 4 ,
(b) exactly 4 . - Use a suitable approximation to the Poisson distribution to find the probability that, in a year consisting of 50 working weeks, the estate agent handles more than 165 house sales.
- One of the conditions needed for the use of a Poisson model to be valid is that house sales are independent of one another.
(a) Explain, in non-technical language, what you understand by this condition.
(b) State another condition that is needed.