A-LevelMathematicsProbability and statistics9709/61 · May/June 2022 · Q17 Marks
The diameters, x millimetres, of a random sample of 200 discs made by a certain machine were recorded. The results are summarised below. n = 200 Σx = 2520 Σx² = 31852
- (a)Calculate a 95% confidence interval for the population mean diameter.[6]
- (b)Jean chose 40 random samples and used each sample to calculate a 95% confidence interval for the population mean diameter. How many of these 40 confidence intervals would be expected to include the true value of the population mean diameter?[1]
Mark scheme
Marking points from the official mark scheme (May/June 2022). The mark or mark type is shown in brackets.
- [B1] Est(u) = 2520/200 [= 12.6] OE
- [M1] Est(σ²) = 200/199 (31852/200 - 12.6²) or 1/199 (31852 - 2520²/200) Allow M1 if 200/199 omitted
- [A1] = 0.5025 or 0.503 or 100/199 CWO or σ = 0.7088 or 0.709
- [B1] z = 1.96
- [M1] '12.6' ± z × √'0.5025'÷200 For expression of correct form Any z but must be z
- [A1] CI = 12.5 to 12.7 (3 sf) CWO Must be an interval Note: Use of biased can score maximum B1 M1 A0 B1 M1 A0
- [B1] 0.95 x 40 [= 38] Give at early stage
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