Every Saturday, a particular community holds a ‘Puzzle' event to raise money for a new Leisure Centre. Competitors attempt to solve a puzzle as quickly as possible. Last Saturday, 600 competitors took part. The times taken to complete the puzzle were normally distributed with mean 32.4 minutes and standard deviation 2.5 minutes.

Mark scheme

Marking points from the official mark scheme (May/June 2025). The mark or mark type is shown in brackets.

1. [M1] OE Using ± standardisation formula, not σ², not σ, no continuity correction. Use of standardisation formula once with 32.4, 2.5 and either 31.2 or 33.6. No continuity correction, not σ², not √σ. Implied by either ± 1.2/2.5 or 1.2/2.5 seen.
2. [M1] Calculating the correct probability area (leading to their final probability). This may be implied by the correct or appropriate probability area.
3. [A1] 0.3688
4. [B1 FT] FT their 4-figure probability to obtain a single integer answer. No approximation indicated, condone use of 3sf probability here if more accurate answer seen earlier.
5. [M1] One term of the form ⁹Cx (p)ˣ (1-p)⁹⁻ˣ, 0 < p < 1, x ≠ 0 or 9.
6. [A1] Correct un-simplified expression. Condone omission of last bracket only. If both brackets omitted in un-simplified expression, allow recovery for final stated calculation of 1 – 0.07434... or better.
7. [B1] 0.925 < p ≤ 0.926 from correct working.
8. [B1] 48 and 19.2 (CAO) seen, allow un-simplified. May be in standardisation formula. (4.38178... to at least 4SF identified as σ implies correct variance). Do not condone clear incorrect identification.
9. [M1] Substituting their 48 and their 19.2 into the standardising formula (any number for 50.5), allow σ² or √σ.
10. [M1] Use continuity correction 49.5 or 50.5 in their standardisation formula. Note: If no working ±2.5/√19.2 or ±2.5/4.382 seen gains B2.
11. [M1] Appropriate probability area, from final process, must be a probability. May be implied by a sketch of the required probability area. Expect final answer < 0.5.
12. [A1] AWRT