N2013 P2 Q7

On average one in \(20\) packets of a breakfast cereal contains a free gift. Jack buys \(n\) packets from a supermarket. The number of these packets containing a free gift is the random variable \(F\).

1. State, in context, two assumptions needed for \(F\) to be well modelled by a binomial distribution.[2]

Assume now that F has a binomial distribution.

2. Given that \(n=20\), find \(\mathrm P(F=1)\).[1]
3. Given instead that \(n=60\), use a suitable approximation to find the probability that \(F\) is at least \(5\). State the parameter(s) of the distribution that you use.[3]