A-LevelMathematicsProbability and statistics9709/63 · Oct/Nov 2017 · Q712 Marks

Josie aims to catch a bus which departs at a fixed time every day. Josie arrives at the bus stop T minutes before the bus departs, where T ~ N(5.3, 2.1²).

(i)Find the probability that Josie has to wait longer than 6 minutes at the bus stop.[3]
(ii)On 5% of days Josie has to wait longer than x minutes at the bus stop. Find the value of x.[3]
(iii)Find the probability that Josie waits longer than x minutes on fewer than 3 days in 10 days.[3]
(iv)Find the probability that Josie misses the bus.[3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.

[M1] Standardising, no continuity correction, no sq, no sq rt
[M1] Correct area 1 – Φ (<0.5), final solution
[A1] = 0.370 or 0.369
[B1] ± 1.645
[M1] Standardising with t = 0, no continuity correction, allow sq, sq rt. Must be equated to a z-value
[A1] x = 8.75 or 8.755 or 8.7545
[M1] Bin term 10Cx p*(1-p)10-x
[M1] Correct unsimplified answer
[A1] = 0.988 (0.9885 to 4 sf)
[*M1] Seeing t linked to zero
[DM1] Standardising with t = 0, no continuity correction, no sq, no sq rt
[A1] = 0.0058

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