A-LevelMathematicsProbability and statistics9709/61 · May/June 2020 · Q16 Marks
The lengths, X centimetres, of a random sample of 7 leaves from a certain variety of tree are as follows. 5.2 4.8 5.5 6.1 4.8 3.9 4.4 It is now given that the true value of the population variance of X is 0.55, and that X has a normal distribution.
- (a)Calculate unbiased estimates of the population mean and variance of X.[3]
- (b)Find a 95% confidence interval for the population mean of X.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.
- [B1] Σχ = 34.7 = 4.9571 or 4.96 (3 sf)
- [M1] (Σχ² = 175.15) 7/6("175.15" - "4.9571"²)
- [A1] 0.523 (3 sf)
- [M1] '4.96'±zx 0.523/7 (FT their mean and standard deviation)
- [B1] z = 1.96
- [A1] 4.42 to 5.49 (3 sf)
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