8. A cloth manufacturer knows that faults occur randomly in the production process at a rate of 2 every 15 metres.
- Find the probability of exactly 4 faults in a 15 metre length of cloth.
- Find the probability of more than 10 faults in 60 metres of cloth.
A retailer buys a large amount of this cloth and sells it in pieces of length \(x\) metres. He chooses \(x\) so that the probability of no faults in a piece is 0.80
- Write down an equation for \(x\) and show that \(x = 1.7\) to 2 significant figures.
The retailer sells 1200 of these pieces of cloth. He makes a profit of 60p on each piece of cloth that does not contain a fault but a loss of \(\pounds 1.50\) on any pieces that do contain faults.
- Find the retailer's expected profit.