A-LevelMathematicsProbability and statistics9709/62 · Feb/Mar 2024 · Q14 Marks
The lengths, Xcm, of a sample of 100 insects of a certain type were summarised as follows. n = 100 Σx = 36.8 Σχ² = 17.34
- (a)Calculate unbiased estimates for the population mean and variance of X.[3]
- (b)State a necessary condition for the estimates found in part (a) to be reliable.[1]
Mark scheme
Marking points from the official mark scheme (Feb/Mar 2024). The mark or mark type is shown in brackets.
- [B1] est(μ) = 0.368 Oe.
- [M1] est(σ²) = (100/99) (17.34 - (36.8/100)²) or (1/99) (17.34 - 36.8²/100) For use of a correct formula (ft their μ).
- [A1] = 0.0384 (3 sf)
- [B1] Must be a random sample. E.g. Values must have been randomly selected. Sample should be representative of the population. All values should have equal chance of being selected. It should be an unbiased sample. Independent sample/insect lengths are independent of one another. ISW
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