A-LevelMathematicsProbability and statistics9709/62 · Oct/Nov 2025 · Q38 Marks
The times, in minutes, taken by students to complete a test have mean μ and standard deviation σ. The times taken by a random sample of 100 students are noted and are used to calculate a 95% confidence interval for μ.
- (a)Given that the end points of the 95% confidence interval are 31.02 and 33.98, correct to 4 significant figures, calculate the value of σ.[3]
- (b)The calculation of the confidence interval required the use of the Central Limit theorem. Explain why it is valid to use the Central Limit theorem in this case.[1]
- (c)A researcher calculates a number, r, of 95% confidence interval for μ. Find the largest value of r such that the probability that all r confidence intervals contain the true value of μ is greater than 0.5.[4]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.
- [1] (a) Sample mean = 32.5 soi or Width = 2.96
- [1] (a) 32.5+ 1.96 × σ/√100 = 33.98 or 2.96 = 2 × 1.96 × σ/√100
- [1] (a) σ = 7.55 (3 sf)
- [1] (b) Because the sample size is large.
- [1] (c) 0.95^r > 0.5
- [1] (c) rln 0.95 > ln 0.5
- [1] (c) r< 13.5....
- [1] (c) Largest value of r is 13
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