A-LevelMathematicsProbability and statistics9709/62 · May/June 2025 · Q610 Marks

Use suitable approximating distributions to answer the following.

(a)(i)The random variable W has the distribution B(700, 0.005). Find P(W ≥ 4).[3]
(a)(ii)Two values of W are chosen at random. Find the probability that the sum of these two values is less than 3.[3]
(b)The random variable X has the distribution Po(200). Use a suitable approximating distribution to find P(X > 205).[4]

Mark scheme

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

[B1] (λ=) 3.5
[M1] Any λ. Expression or terms must be seen. Allow one end error. Accept fully correct Σ notation.
[A1] = 0.463 (3 sf) SC Unsupported correct answer scores B1B1 SC Use of Binomial scores B1 for 0.464. Note: Use of Normal can score B1 for mean =3.5.
[B1] (λ=) 7 Seen.
[M1] Any λ. Expression or terms must be seen. Allow one end error Accept fully correct ∑ notation. Accept combination method for Poisson (6 combinations) allow 6 correct combinations identified B1, attempt to calculate and combine at least four correct combinations M1.
[A1] = 0.0296 (3 sf) SC Unsupported correct answer scores B1B1. SC Use of Bin B1 for 0.0294. Note: Use of Normal can score B1 for mean =7.
[M1] N(200, 200) SOI.
[M1] 205.5-200 / sqrt(200) [= 0.38891] Allow with omitted or incorrect cc.
[M1] For finding area consistent with their values.
[A1] = 0.349 (3 sf)

On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.