A-LevelMathematicsProbability and statistics9709/61 · Oct/Nov 2021 · Q15 Marks

It is known that the height H, in metres, of trees of a certain kind has the distribution N(12.5, 10.24). A scientist takes a random sample of 25 trees of this kind and finds the sample mean, H, of the heights.

Mark scheme

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

[B1] N(12.5, ....)
[B1] Variance = 0.4096 (Accept 0.410 (3sf), condone 10.24/25)
[M1] (13-'12.5') / √'0.4096' [= 0.781] (For standardising with their values. Accept standardising with 12.)
[M1] Φ('0.781') – (1 – Φ(‘0.781')) (For attempting to find their central area.)
[A1] 0.565 (3sf)

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Topic: Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 5 marks.
Source: A-Level Mathematics, Oct/Nov 2021 Paper 6 Variant 1, question 1.

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