A-LevelMathematicsProbability and statistics9709/62 · May/June 2024 · Q34 Marks

A student wishes to estimate the proportion, p, of students at her college who have exactly one brother. She surveys a random sample of 50 students at her college and finds that 18 of them have exactly one brother. She calculates an approximate α% confidence interval for p and finds that the lower limit of the confidence interval is 0.244 correct to 3 significant figures.

Mark scheme

Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.

[M1] 18/50 - z * √( (18/50)(32/50) / 50 ) = 0.244 Use of correct equation.
[A1] z = 1.709 or 1.708 Accept 1.71 if nothing better seen.
[M1] Φ⁻¹('1.709') = 0.956 ; 1 – 2(1 – ‘0.956') [= 0.912] Attempt area above or below their 1.709 and use correct method to find α.
[A1] α = 91 Allow α = 91% 0.91 or 91.2 score A0.

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Topic: Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 4 marks.
Source: A-Level Mathematics, May/June 2024 Paper 6 Variant 2, question 3.

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