One of a group of three students is to be chosen at random. The times, in minutes, taken by students to complete a test are normally distributed with mean 125 and variance 50. Two students are chosen at random.

Mark scheme

Marking points from the official mark scheme (May/June 2025). The mark or mark type is shown in brackets.

1. [B1] E.g. 1-2: choose student 1; 3-4: choose student 2; 5-6: choose student 3. Must be un-ambiguous i.e. if no example, need to say 2 different numbers per person AND different to the other two people so that all 6 numbers on dice used. Other correct methods may be seen. Note: must be a single throw.
2. [B1] E(D) = 0, Var(D) = 100 Or E(D)=±12.
3. [M1] For standardising with their E(D) and Var(D) Must be from a combination attempt, ignore cc attempts. [= 1.2]
4. [M1] For finding area consistent with their values.
5. [A1] SOI by correct final answer.
6. [A1FT] FT their 0.115 (as long as '0.115' < 0.5 i.e. final prob not bigger than 1).