A-LevelMathematicsProbability and statistics9709/62 · Oct/Nov 2022 · Q17 Marks
Each of a random sample of 80 adults gave an estimate, h metres, of the height of a particular building. The results were summarised as follows. n = 80 Σh = 2048 Σh² = 52760
- (a)Calculate unbiased estimates of the population mean and variance.[3]
- (b)Using this sample, the upper boundary of an α% confidence interval for the population mean is 26.0. Find the value of α.[4]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.
- [B1] 1(a) Est μ = 25.6 or 2048/80 or 128/5
- [M1] 1(a) Substitution into a correct formula. Biased 4.14 scores M0.
- [A1] 1(a) = 4.19 (3 sf) or 1656/395
- [M1] 1(b) Use of correct equation with their values.
- [A1] 1(b) z = 1.748 or 1.747 Accept 3sf. FT Biased z = 1.758.
- [M1] 1(b) (Φ('1.748') = 0.960) ‘0.960’ – (1 – ‘0.960’) Correct area using their values.
- [A1] 1(b) α = 92.0 or 91.9 Allow 92 . FT Biased 92.1. A final answer of 0.92 or 0.919 scores A0.
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