N2008 P2 Q9

A shop sells two types of piano, ‘grand’ and ‘upright’. The mean number of grand pianos sold in a week is 1.8. Use a Poisson distribution to find the probability that in a given week at least 4 grand pianos are sold.[2]

The mean number of upright pianos sold in a week is 2.6. The sales of the two types of piano are independent. Use a Poisson distribution to find the probability that in a given week the total number of pianos sold is exactly 4.[2]

Use a normal approximation to the Poisson distribution to find the probability that the number of grand pianos sold in a year of 50 weeks is less than 80.[4]

Explain why the Poisson distribution may not be a good model for the number of grand pianos sold in a year.[2]