A-LevelMathematicsProbability and statistics9709/51 · May/June 2024 · Q27 Marks

The lengths of the tails of adult raccoons of a certain species are normally distributed with mean 28 cm and standard deviation 3.3 cm.

(a)Find the probability that a randomly chosen adult raccoon of this species has a tail length between 23 cm and 35 cm.[4]
(b)The masses of adult raccoons of this species are normally distributed with mean 8.5 kg and standard deviation σ kg. 75% of adult raccoons of this species have mass greater than 7.6 kg. Find the value of σ.[3]

Mark scheme

Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.

[M1] Using standardisation formula once with 23 or 35, 28 and 3.3, allow σ², allow √σ, no continuity correction.
[A1] One fully correct z standardisation formula.
[M1] Appropriate area Φ, from final process, must be a probability.
[A1] AWRT 0.918
[B1] 0.674 or – 0.674 seen. CAO as critical value.
[M1] Use of the standardisation formula with 7.6, 8.5, σ and a z-value (not 0.75, 0.25, 0.7734, 0.2266, 0.5987 nor 1 – z-value: 0.326, 0.5987). Condone use of ±0.9 / σ
[A1] 1.33 < σ < 1.34

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