A-LevelMathematicsProbability and statistics9709/53 · Oct/Nov 2020 · Q16 Marks
The times taken to swim 100 metres by members of a large swimming club have a normal distribution with mean 62 seconds and standard deviation 5 seconds.
- (a)Find the probability that a randomly chosen member of the club takes between 56 and 66 seconds to swim 100 metres.[3]
- (b)13% of the members of the club take more than t minutes to swim 100 metres. Find the value of t.[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.
- [M1] Using ± standardisation formula at least once, no √σ or σ², allow continuity correction
- [M1] Appropriate area Φ, from standardisation formula in final solution
- [A1] 0.673
- [B1] ±(1.126 – 1.127) seen, 4 sf or more
- [M1] z-value = ± (60t-62)/5, condone z-value = ± (t-62)/5 no continuity correction, condone √σ or σ²
- [A1] CAO
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