4. The number of houses sold by an estate agent follows a Poisson distribution, with a mean of 2 per week.
- Find the probability that in the next 4 weeks the estate agent sells,
- exactly 3 houses,
- more than 5 houses.
The estate agent monitors sales in periods of 4 weeks.
- Find the probability that in the next twelve of these 4 week periods there are exactly nine periods in which more than 5 houses are sold.
The estate agent will receive a bonus if he sells more than 25 houses in the next 10 weeks.
- Use a suitable approximation to estimate the probability that the estate agent receives a bonus.