A-LevelMathematicsProbability and statistics9709/61 · May/June 2025 · Q27 Marks
The random variable X has the distribution B(8, 3/4). A random sample of 100 values of X is chosen, and the sample mean, X̅, is found.
- (a)Find P(X̅ > 6.2). You are not expected to use a continuity correction.[6]
- (b)State why the Central Limit Theorem was needed in the calculation in part (a).[1]
Mark scheme
Marking points from the official mark scheme (May/June 2025). The mark or mark type is shown in brackets.
- [B1] Normal used with a mean of 6.
- [M1] Var of 1.5 (or sd found).
- [M1] For standardising. Must have √100. Ignore incorrect continuity correction (correct cc if used is 1/2n).
- [A1] Or accept 1.674 with correct cc.
- [M1] For area consistent with their working
- [A1] Or accept 0.0471 with correct cc (scores full marks).
- [B1] Population (X) is not normally distributed / Population (X) is Binomial OE. Accept underlying distribution.
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