1. (a) Explain why it is often useful to take samples as a means of obtaining information.
   (b) Briefly define the term sampling frame.
   (c) Suggest a suitable sampling frame for a sample survey on a proposal to install speed humps on a road.
2. An insurance company conducts its business by using a Call Centre. The average number of calls per minute is \(3 \cdot 5\). In the first minute after a TV advertisement is shown, the number of calls received is 7 .
   (a) Stating your hypotheses carefully, and working at the \(5 \%\) significance level, test whether the advertisement has had an effect.
   (b) Find the number of calls that would be required in the first minute for the null hypothesis to be rejected at the \(0.1 \%\) significance level.
3. On average, \(35 \%\) of the candidates in a certain subject get an A or B grade in their exam. In a class of 20 students, find the probability that
   (a) less than 5 get A or B grades,
   (b) exactly 8 get A or B grades.

Five such classes of 20 students are combined to sit the exam.
(c) Use a suitable approximation to find the probability that less than a quarter of the total get A or B grades.