A-LevelMathematicsProbability and statistics9709/62 · Feb/Mar 2022 · Q59 Marks

The heights of buildings in a large city are normally distributed with mean 18.3m and standard deviation 2.5 m.

(a)Find the probability that the total height of 5 randomly chosen buildings in the city is more than 95 m.[4]
(b)Find the probability that the difference between the heights of two randomly chosen buildings in the city is less than 1 m.[5]

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2022). The mark or mark type is shown in brackets.

[B1] Mean = 5×18.3 and Variance = 5×2.5² [= N(91.5, 31.25)] SOI
[M1] 95-'91.5 / √'31.25' [= 0.626] FT their mean and variance
[M1] 1 – Ф('0.626') For finding area consistent with their values
[A1] 0.266 (3 sf)
[B1] E(D) = 0 Or E(D- 1) = −1
[B1] Var(D) = 2.5² × 2 [= 12.5]
[M1] 1-0 / √'12.5' [= 0.283] or -1-0 / √'12.5' [= -0.283] FT their E and Var
[M1] Φ('0.283') – (1 – (0.283)) [= 0.6115 – 0.3885] For finding area consistent with their values
[A1] 0.223 (3 sf)

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Topic: Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 9 marks.
Source: A-Level Mathematics, Feb/Mar 2022 Paper 6 Variant 2, question 5.

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