The random variable X has the distribution B(400, 0.01).

Mark scheme

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

1. [M1] (a) Var(X) = 400 × 0.01 × 0.99 (= 3.96)
2. [M1] (a) Var(4X+2) = 16 × Var(X); For 16 × their Var(X)
3. [A1] (a) 63.36; Accept 63.4
4. [B1] (b)(i) Po(4)
5. [B1] (b)(i) n = 400 > 50 and either np = 4 < 5 or p=0.01 < 0.1; Must quote values 400 and 4 or clearly see n=400 and np=4 (or p=0.01) in working
6. [M1] (b)(ii) e^-4 (4^2/2! + 4^3/3! + 4^4/4! + 4^5/5!); FT their '4'; Allow one end error; FT from (b)(i) Use of Normal allow M1 for attempt at standardising (with correct continuity correction) using their N(4,3.96) and attempt at probability. FT from (b)(i) Use of Binomial allow M1 for attempt at P(2,3,4,5) Binomial terms clearly seen and added
7. [A1] (b)(ii) 0.694 (3 sf); CWO; SC B1 only for unsupported answer of 0.694