A-LevelMathematicsProbability and statistics9709/61 · Oct/Nov 2019 · Q710 Marks

The shortest time recorded by an athlete in a 400 m race is called their personal best (PB). The PBs of the athletes in a large athletics club are normally distributed with mean 49.2 seconds and standard deviation 2.8 seconds.

(i)Find the probability that a randomly chosen athlete from this club has a PB between 46 and 53 seconds.[4]
(ii)It is found that 92% of athletes from this club have PBs of more than t seconds. Find the value of t.[3]
(iii)Three athletes from the club are chosen at random. Find the probability that exactly 2 have PBs of less than 46 seconds.[3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.

[M1] Using ± standardisation formula for either 46 or 53, no continuity correction, σ² or √σ
[A1] Both standardisations correct unsimplified
[M1] Correct final area
[A1] 0.786
[B1] ±1.406 seen
[M1] An equation using ± standardisation formula with a z-value, condone σ² or √σ
[A1] 45.3
[M1] Calculated or ft from (i)
[M1] 3(1-p)p², 0<p<1
[A1] 0.0419

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