A-LevelMathematicsProbability and statistics9709/51 · May/June 2021 · Q69 Marks

In Questa, 60% of the adults travel to work by car.

(a)A random sample of 12 adults from Questa is taken. Find the probability that the number who travel to work by car is less than 10.[3]
(b)A random sample of 150 adults from Questa is taken. Use an approximation to find the probability that the number who travel to work by car is less than 81.[5]
(c)Justify the use of your approximation in part (b).[1]

Mark scheme

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

[M1] One term: 12Cx p*(1 – p)12-x for 0 < x < 12, any p allowed.
[A1] Correct unsimplified expression, or better.
[A1] AWRT
[B1] Correct mean and variance. Accept evaluated or unsimplified
[M1] Substituting their mean and variance into standardisation formula (with a numerical value for 80.5), allow σ², √σ, but not µ ± 0.5
[M1] Using continuity correction 80.5 or 81.5
[M1] Appropriate area Φ, from final process, must be probability
[A1] AWRT
[B1] At least nq evaluated and statement >5 required

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About this question

Topic

Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 9 marks.

Source

A-Level Mathematics, May/June 2021 Paper 5 Variant 1, question 6.

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