The number, X, of books received at a charity shop has a constant mean of 5.1 per day.

Mark scheme

Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.

1. [1] Books received independently or singly or randomly. OE. Must be in context. If more than one condition given, ignore extras.
2. [1] e⁻¹⁵.³ × 15.3¹⁰ / 10! Allow incorrect λ.
3. [1] = 0.0439 (3sf) SC No working shown but correct answer seen scores B1.
4. [1] N(153, 153) Seen or implied.
5. [1] (180.5-153) / √153 [= 2.223] For standardising with their values (can be implied). Allow with wrong or missing continuity correction.
6. [1] 1 – Φ('2.223') For correct probability area consistent with their values.
7. [1] = 0.0131 (3sf)
8. [1] (λ =) 5.1 + 2.5 [= 7.6] Give at early stage (seen or implied).
9. [1] 1 - e⁻⁷.⁶(1 + 7.6 + 7.6²/2 + 7.6³/3!) = 1 - e⁻⁷.⁶(1 + 7.6 + 28.88 + 73.16) = 1 – (0.0005005+0.003803+0.01445+0.03661) Allow incorrect λ. Allow one end error. Must see an expression (accept correct sigma notation).
10. [1] = 0.945 (3sf) SC No working, 0.945 B1(could be implied) SC B1.