A mathematical puzzle is given to a large number of students. The times taken to complete the puzzle are normally distributed with mean 14.6 minutes and standard deviation 5.2 minutes.

Mark scheme

Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.

1. [M1] Use of ± standardisation formula with 20, 14.6 and 5.2 not σ², not √σ, no continuity correction.
2. [M1] Calculating the appropriate probability area (leading to their final answer).
3. [A1] 0.1496, 0.149 < p < 0.15[0] . Only dependent on the 2nd M mark so M0M1A1 possible. SC B1 for 0.149 < p < 0.15[0] if M0M0A0 awarded.
4. [B1 FT] Strict FT their at least 4-figure probability seen anywhere (give BOD if they go on to use 0.150). Final answer must be positive integer, no approximation or rounding stated.
5. [B1] -0.843 < z₁ < -0.841 or 0.841 < z₁ < 0.843.
6. [B1] -0.441 < z₂ < -0.439 or 0.439 < z₂ < 0.441.
7. [M1] Use of the standardisation formula once with μ, σ and a z-value (not 0.20, 0.80, 0.67, 0.23, 0.5793, 0.7881, 0.7486, 0.591 or 1-z i.e. 0.158 etc.). Condone continuity correction ±0.05, not σ²,√σ.
8. [M1] Solve using the elimination method, substitution method or other appropriate approach to obtain values for both μ and σ.
9. [A1] AWRT 22.9, 9.95 .