A-LevelMathematicsProbability and statistics9709/62 · May/June 2021 · Q68 Marks
The heights, h centimetres, of a random sample of 100 fully grown animals of a certain species were measured. The results are summarised below. n = 100 Σh = 7570 Σh² = 588 050
- (a)Find unbiased estimates of the population mean and variance.[3]
- (b)Calculate a 99% confidence interval for the mean height of animals of this species.[3]
- (c)Four random samples were taken and a 99% confidence interval for the population mean, μ, was found from each sample. Find the probability that all four of these confidence intervals contain the true value of μ.[2]
Mark scheme
Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.
- [B1] (a) est (μ) = 7570/100 (= 75.7)
- [M1] (a) est(σ²) = (100/99) (Σh²/100 - '75.7'²) or (1/99) (588050 - 7570²/100) or (100/99) (588050/100 - '75.7'²) [= 151.525]; Attempted (Note: Biased variance (150.01) scores M0)
- [A1] (a) = 152 (3 sf) Or 15001/99
- [M1] (b) '75.7' ± z √('151.525'/100); For expression of correct form. Must be a z value. Condone just + or just -.
- [B1] (b) z = 2.576; Accept 2.574 to 2.579
- [A1 FT] (b) 72.5 to 78.9; FT biased variance only; Must be an interval
- [B1] (c) 0.99^4
- [B1] (c) 0.961 (3 sf)
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