6. Minor defects occur in a particular make of carpet at a mean rate of 0.05 per \(\mathrm { m } ^ { 2 }\).
- Suggest a suitable model for the distribution of the number of defects in this make of carpet. Give a reason for your answer.
A carpet fitter has a contract to fit this carpet in a small hotel. The hotel foyer requires \(30 \mathrm {~m} ^ { 2 }\) of this carpet. Find the probability that the foyer carpet contains
- exactly 2 defects,
- more than 5 defects.
The carpet fitter orders a total of \(355 \mathrm {~m} ^ { 2 }\) of the carpet for the whole hotel.
- Using a suitable approximation, find the probability that this total area of carpet contains 22 or more defects.
(6)