A-LevelMathematicsProbability and statistics9709/63 · May/June 2020 · Q510 Marks
Sunita has a six-sided die with faces marked 1, 2, 3, 4, 5, 6. The probability that the die shows a six on any throw is p. Sunita throws the die 500 times and finds that it shows a six 70 times.
- (a)Calculate an approximate 99% confidence interval for p.[4]
- (b)Sunita believes that the die is fair. Use your answer to part (a) to comment on her belief.[1]
- (c)Sunita uses the result of her 500 throws to calculate an α% confidence interval for p. This interval has width 0.04. Find the value of α.[5]
Mark scheme
Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.
- [B1] (a) p = 70/500 or 0.14
- [B1] (a) z=2.576
- [M1] (a) “0.14” ± z × √(“0.14”(1–“0.14”)/500)
- [A1] (a) 0.100 to 0.180
- [B1] (b) 0.1666... is within confidence interval / Belief supported or justified
- [M1] (c) z × √(“0.14”(1–“0.14”)/500) = 0.02
- [A1] (c) z = 1.289
- [M1] (c) Φ(‘1.289’) = 0.9013
- [M1] (c) α = ‘0.9013’ – (1 – ‘0.9013’)
- [A1] (c) 80.3% (3 sf)
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