A-LevelMathematicsProbability and statistics9709/53 · Oct/Nov 2020 · Q48 Marks

The 1300 train from Jahor to Keman runs every day. The probability that the train arrives late in Keman is 0.35.

(a)For a random sample of 7 days, find the probability that the train arrives late on fewer than 3 days.[3]
(b)A random sample of 142 days is taken. Use an approximation to find the probability that the train arrives late on more than 40 days.[5]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.

[M1] Binomial term of form ⁿCx pˣ (1-p)ⁿ⁻ˣ, 0<p<1, any p, x ≠ 0, 7
[A1] Correct unsimplified answer
[A1] 0.532
[B1] Correct unsimplified np and npq (condone σ = 5.684 evaluated)
[M1] Substituting their µ and σ (no √σ or σ²) into standardisation formula with a numerical value for '40.5'
[M1] Using either 40.5 or 39.5 within a standardisation formula
[M1] Appropriate area Ф, from standardisation formula P(z >...) in final solution, must be probability
[A1] Correct final answer

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.

Topic: Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 8 marks.
Source: A-Level Mathematics, Oct/Nov 2020 Paper 5 Variant 3, question 4.

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