A-LevelMathematicsProbability and statistics9709/61 · Oct/Nov 2021 · Q35 Marks

A random sample of 75 students at a large college was selected for a survey. 15 of these students said that they owned a car. From this result an approximate a% confidence interval for the proportion of all students at the college who own a car was calculated. The width of this interval was found to be 0.162.

Mark scheme

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

[B1] est(p) = 0.2 accept 15/75 (SOI)
[M1] 2z × √(0.2×0.8 / 75) = 0.162 (Expression of the correct form. Condone missing 2x.)
[A1] z = 0.081 × √(75 / (0.2×0.8)) = 1.754 (Correct z. Condone 3sf accuracy.)
[M1] Φ('1.754') = 0.96[03] (OE. Using their z to find alpha.)
[A1] α = 92 (Following correct working.)

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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 3.

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