Customers arrive at a particular shop at random times. It has been found that the mean number of customers who arrive during a 5-minute interval is 2.1.

Mark scheme

Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.

1. [M1] (a) e^-4.2 × 4.2^4 / 4!; P(4), allow any λ
2. [A1] (a) 0.194 (3 sf); As final answer. SC Unsupported correct answer scores B1 only.
3. [M1] (b) 1 – e^-8.4 (1+8.4+8.4²/2! + 8.4³/3!); Allow M1 with incorrect λ. Accept one end error.
4. [A1] (b) 0.968 (3 sf); As final answer. SC Unsupported correct answer scores B1 only.
5. [M1] (c) N(50.4, 50.4); SOI
6. [M1] (c) (39.5-50.4) / √50.4 [= -1.535]; Allow wrong or no continuity correction. Must have √
7. [M1] (c) Φ('-1.535') = 1 – Ф(‘1.535'); For correct probability area consistent with their working.
8. [A1] (c) 0.0624 (3 sf) or 0.0623