ACJC Binomial Distribution Assignment Q1

Batteries are packed in boxes of \(200\), and on average \(0.5\%\) of all batteries are defective.

1. A box which contains one or more defective batteries is substandard. Show that the probability that a randomly chosen box will be substandard is \(0.633\), correct to three decimal places.[2]
2. A truck-load consists of \(10\) boxes, randomly chosen. If more than \(8\) boxes on any particular truck-load are substandard then the truck-load fails the quality test. A random sample of \(14\) truck-loads is taken. What is the probability that exactly \(2\) of these truck-loads will fail the quality test?[4]
3. Explain why a binomial distribution is appropriate for modelling the number of defective batteries in a box.[2]