Assume that precisely \(30 \%\) of the population will be voting Liberal Democrat at the next election. You are conducting a poll. What is the probability that between 27 and \(33 \%\) of a random sample will tell you that they are going to vote Liberal Democrat, if ...

(a) you poll 10 people;

(b) you poll 100 people;

(c) you poll 1000 people;

(d) you poll 10000 people?