A-LevelMathematicsProbability and statistics9709/52 · May/June 2021 · Q59 Marks
Every day Richard takes a flight between Astan and Bejin. On any day, the probability that the flight arrives early is 0.15, the probability that it arrives on time is 0.55 and the probability that it arrives late is 0.3.
- (a)Find the probability that on each of 3 randomly chosen days, Richard's flight does not arrive late.[1]
- (b)Find the probability that for 9 randomly chosen days, Richard's flight arrives early at least 3 times.[3]
- (c)60 days are chosen at random. Use an approximation to find the probability that Richard’s flight arrives early at least 12 times.[5]
Mark scheme
Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.
- B1 Evaluated WWW
- M1 One term: ⁹Cx pˣ (1 – p)⁹⁻ˣ for 0 < x < 9, any 0 <p<1
- A1 Correct expression, accept unsimplified.
- A1 0.1408 ≤ ans ≤ 0.141, award at most accurate value.
- B1 Correct mean and variance, allow unsimplified. (2.765 ≤ σ ≤ 2.77 imply correct variance)
- M1 Substituting their mean and variance into standardisation formula (any number for 11.5), not σ² or √σ
- M1 Using continuity correction 11.5 or 12.5 in their standardisation formula.
- M1 Appropriate area Φ, from final process, must be probability.
- A1 Final AWRT
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