2013 HCI P2 Q6 [Modified]
2013 HCI P2 Q6 [Modified]
In a carton of apples, a sample of \(8\) apples is taken and examined for spoilt apples.
- State, in context, an assumption for the number of spoilt apples in the sample to be modelled by a binomial distribution.
The number of spoilt apples in a random sample of size \(8\) may be modelled by the distribution \(\mathrm{B}(8, p)\). If at least \(2\) apples in a sample are found to be spoilt, the carton is rejected. It is known that the probability of a carton being rejected is \(0.04\).
- Write down an equation satisfied by \(p\) and find the value of \(p\).
- \(60\) cartons of apples are loaded onto a lorry. Find the probability that more than \(56\) cartons loaded onto the lorry are not rejected.
Solution:
Solution locked
680+ questions here come with free worked solutions. A free account saves your questions and progress; this one needs a course plan.
Create a free account to practise similar questions.
Answer:(i) Independent spoilage events with a constant spoilage probability. (ii) \((1-p)^8+8p(1-p)^7=0.96\), \(p=0.0410\). (iii) \(0.781\).
Need help? Join our JC Math tuition classes.
Learn more