A-LevelMathematicsProbability and statistics9709/62 · Oct/Nov 2023 · Q16 Marks

A random variable X has the distribution Po(25).

(a)Use the normal approximation to the Poisson distribution to find P(X > 30).[4]
(b)A random variable Y has the distribution B(100, p) where p < 0.05. Use the Poisson approximation to the binomial distribution to write down an expression, in terms of p, for P(Y < 3).[2]

Mark scheme

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

[B1] X~N(25, 25) soi
[M1] Standardising with their values. Allow with missing or incorrect continuity correction. (30.5-25)/√25 [= 1.1]
[M1] For area consistent with their working. 1 – Φ('1.1')
[A1] = 0.136 (3 sf)
[M1] For Po(100p) expression. Accept un-simplified terms (e.g. p/0! For M1). Allow one end error (e.g. for correct with extra term e-100p x (100p)³/3! oe), or brackets omitted. e-100p (1+100p+(100p)²/2!)
[A1] Must have brackets. Allow with or without ! sign (but not 0! or p⁰). ISW once a fully correct answer seen. or e-100p + e-100p x 100p + e-100p x (100p)²/2! or e-100p(1 + 100p + 5000p²) oe

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.

About this question

Topic

Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 6 marks.

Source

A-Level Mathematics, Oct/Nov 2023 Paper 6 Variant 2, question 1.

Questions and mark schemes are from past examination papers and remain the copyright of the exam board. How Oracle Prep builds its content