A-LevelMathematicsProbability and statistics9709/62 · Feb/Mar 2021 · Q17 Marks

A construction company notes the time, t days, that it takes to build each house of a certain design. The results for a random sample of 60 such houses are summarised as follows. Στ = 4820 Στ² = 392 050

(a)Calculate a 98% confidence interval for the population mean time.[6]
(b)Explain why it was necessary to use the Central Limit theorem in part (a).[1]

Mark scheme

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

[B1] Est(u) = 4820/60 or 241/3 or 80.3 (3 sf)
[M1] Est(σ²) = 60/59 (392050/60 - (4820/60)²) to 82.0904 or 14530/177 to 82.635 or SD = 9.0604 to 9.0904 (3sf)
[B1] z = 2.326
[M1] 4820/60 ± z x '82.0904'/60
[A1] 77.6 to 83.1 (3 sf)
[B1] Population distribution of times unknown

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Topic: Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 7 marks.
Source: A-Level Mathematics, Feb/Mar 2021 Paper 6 Variant 2, question 1.

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