Solve a rejection probability and then model accepted cartons

In a carton of apples, a sample of 8 apples is taken and examined for spoilt apples.

(i) State, in context, an assumption for the number of spoilt apples in the sample to be modelled by a binomial distribution.1 mark

The number of spoilt apples in a random sample of size 8 may be modelled by the distribution $B(8,p)$. 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.

(ii) Write down an equation satisfied by $p$ and find the value of $p$.3 marks

(iii) 60 cartons of apples are loaded onto a lorry. Find the probability that more than 56 cartons loaded onto the lorry are not rejected.3 marks