A-LevelMathematicsProbability and statistics9709/52 · Oct/Nov 2020 · Q39 Marks

Pia runs 2 km every day and her times in minutes are normally distributed with mean 10.1 and standard deviation 1.3.

(a)Find the probability that on a randomly chosen day Pia takes longer than 11.3 minutes to run 2 km.[3]
(b)On 75% of days, Pia takes longer than t minutes to run 2 km. Find the value of t.[3]
(c)On how many days in a period of 90 days would you expect Pia to take between 8.9 and 11.3 minutes to run 2 km?[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, no √σ or σ², continuity correction
[M1] Appropriate area Φ, from standardisation formula P(z>...) in final solution
[A1] 0.1779...
[B1] ±0.674 seen (critical value)
[M1] An equation using ±standardisation formula with a z-value, condone √σ or σ², continuity correction.
[A1] AWRT. Only dependent on M1
[B1 FT] FT from their 3(a) < 0·5 or correct, accept unevaluated probability OE
[M1] 90 × their p seen, 0 < p <1
[A1 FT] Accept 57 or 58, not 57·0 or 58·0, no approximation/rounding stated FT must be an integer value

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