4. The random variable \(X \sim \mathrm {~B} ( 27,0.35 )\)
- Find
- \(\mathrm { P } ( X = 10 )\)
- \(\mathrm { P } ( 12 \leqslant X < 15 )\)
Historical records show that the proportion of defective items produced by a machine is 0.12
Following a maintenance service of the machine, a random sample of 60 items is taken and 3 defective items are found.
- Carry out a suitable test to determine whether the proportion of defective items produced by the machine has decreased following the maintenance service. You should state your hypotheses clearly and use a \(5 \%\) level of significance.
- Write down the \(p\)-value for your test in part (b)