In Jimpuri the weights, in kilograms, of boys aged 16 years have a normal distribution with mean 61.4 and standard deviation 12.3. In Brigville the weights, in kilograms, of boys aged 16 years have a normal distribution. 99% of the boys weigh less than 97.2 kilograms and 33% of the boys weigh less than 55.2 kilograms.

Mark scheme

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

1. M1 Standardising no continuity correction, no square or square root, condone ± standardisation formula
2. M1 Correct area (< 0.5)
3. A1 = 1-0.6153 = 0.385
4. B1 P(<65) = 0.6153 so P(< k) = 0.25 +0.6153 = 0.8653
5. B1 z = ± 1.105 seen or rounding to 1.1
6. M1 standardising allow ±, cc, sq rt, sq. Need to see use of tables backwards so must be a z-value, not 1 – z value.
7. A1 Answers which round to 75.0. Condone 75 if supported.
8. B1 ± 2.326 seen (Use of critical value)
9. B1 ±0.44 seen
10. M1 An equation with a z-value, α σ and 97.2 or 55.2, allow √σ or σ᾽
11. M1 Algebraic elimination α or σ from their two simultaneous equations
12. A1 both correct answers