A-LevelMathematicsProbability and statistics9709/52 · Oct/Nov 2023 · Q35 Marks
A factory produces a certain type of electrical component. It is known that 15% of the components produced are faulty. A random sample of 200 components is chosen.
- (a)Use an approximation to find the probability that more than 40 of these components are faulty.[5]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2023). The mark or mark type is shown in brackets.
- [B1] Mean = 30 and Variance = 25.5 (or Standard Deviation = 5.04975)
- [M1] Substituting their mean and their positive 5.04975 into standardisation formula (any number for 40.5), not their σ² or √their σ.
- [M1] Using continuity correction 39.5 or 40.5 in their standardisation formula.
- [M1] Appropriate area Φ, from final process, must be a probability.
- [A1] 0.0188 (0.01875 < p < 0.0188).
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