2020 CJC P2 Q7

Flyers of a tuition centre for General Paper (GP) tuition are given to JC2 students in a particular college with a large population. On average, \(8\%\) of the JC2 students will sign up for the GP tuition.

1. State, in context, two assumptions needed for the number of JC2 students signing up for the GP tuition to be well modelled by a binomial distribution.[2]

Assume now that the number of JC2 students signing up for the GP tuition follows a binomial distribution.

2. It is given that \(120\) JC2 students receive a copy of the flyer.
   1. Find the probability that more than \(15\) students sign up for the GP tuition.[2]
   2. Find the variance of the number of students signing up for the GP tuition.[1]

Flyers of another tuition centre for Mathematics tuition are given to JC2 students in the same college.

The number of students of students who sign up for the Mathematics tuition is denoted by \(M\). Assume that \(M\) has a distribution \(\mathrm{B}\,(320,\,p)\).

3. It is known that on average the proportion of students who sign up for Mathematics tuition is higher than the proportion of students who signed up for GP tuition. Given that \(P(M=30 \text{ or}\hspace{0.5em} 31)=0.037986\) correct to \(5\) significant figures, find the value of \(p\).[2]