A-LevelMathematicsProbability and statistics9709/63 · May/June 2024 · Q24 Marks
The widths, wcm, of a random sample of 150 leaves of a certain kind were measured. The sample mean of w was found to be 3.12 cm. Using this sample, an approximate 95% confidence interval for the population mean of the widths in centimetres was found to be [3.01, 3.23].
- (a)Calculate an estimate of the population standard deviation.[3]
- (b)Explain whether it was necessary to use the Central Limit theorem in your answer to part (a).[1]
Mark scheme
Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.
- [M1] 3.12 + z x (σ/√150) = 3.23
- [B1] z = 1.96
- [A1] σ ≈ 0.687 (3sf) [cm]
- [B1] Yes, because population [of widths] not given to be normally distributed
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