A-LevelMathematicsProbability and statistics9709/61 · Oct/Nov 2022 · Q37 Marks
Drops of water fall randomly from a leaking tap at a constant average rate of 5.2 per minute.
- (a)Find the probability that at least 3 drops fall during a randomly chosen 30-second period.[3]
- (b)Use a suitable approximating distribution to find the probability that at least 650 drops fall during a randomly chosen 2-hour period.[4]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.
- [B1] λ = 5.2 ÷ 2 [= 2.6]
- [M1] 1-e^-2.6(1 + 2.6 + 2.6^2/2!) or 1 – e^-2.6( 1 + 2.6 +3.38) or 1-(0.07427 +0.1931 +0.2510)
- [B1] = 0.482 (3 sf)
- [B1] N(120×5.2, 120×5.2)
- [M1] (649.5 - their '624') / √their '624'
- [M1] 1- Φ(their '1.021')
- [A1] = 0.154 (3 sf)
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