In a carton of apples, a sample of $8$ apples is taken and examined for spoilt apples. State, in c

Question

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.

Accepted Answer

(i) The probability of obtaining a spoilt apple is constant. Or Obtaining a spoilt apple is independent of other spoilt apples. (ii) ${{(1-p)}^{8}}+8p{{(1-p)}^{7}}=0.96$; $p=0.0410$ (iii) $0.781$

2013 HCI P2 Q6 [Modified]

2013 HCI P2 Q6 [Modified]