A school held a disco for years 9,10 and 11 which was attended by 500 pupils. The pupils were registered as they entered the disco. The disco organisers were keen to assess the success of the event. They designed a questionnaire to obtain information from those who attended.
State one advantage and one disadvantage of using a sample survey rather than a census.
Suggest a suitable sampling frame.
Identify the sampling units.
A piece of string \(A B\) has length 12 cm . A child cuts the string at a randomly chosen point \(P\), into two pieces. The random variable \(X\) represents the length, in cm, of the piece \(A P\).
Suggest a suitable model for the distribution of \(X\) and specify it fully
Find the cumulative distribution function of \(X\).
Write down \(\mathrm { P } ( X < 4 )\).
A manufacturer of chocolates produces 3 times as many soft centred chocolates as hard centred ones.
Assuming that chocolates are randomly distributed within boxes of chocolates, find the probability that in a box containing 20 chocolates there are
equal numbers of soft centred and hard centred chocolates,
fewer than 5 hard centred chocolates.
A large box of chocolates contains 100 chocolates.
Write down the expected number of hard centred chocolates in a large box.