In a large population, the systolic blood pressure (SBP) of adults is normally distributed with mean 125.4 and standard deviation 18.6. Three adults are chosen at random from this population.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.

1. [M1] Use of standardisation formula with 132 and 125.4 substituted, condone continuity correction 132±0.5 and use of 18.6², √18.6
2. [A1] 0.6385 < p ≤ 0.639 If M0 scored, SC B1 for 0.6385 < p < 0.639
3. [B1] 1.1749 < z < 1.175 or – 1.175 < z < -1.1749
4. [M1] 108 and 117 substituted in standardisation formula, no continuity correction, not o², √ o, equated to a z-value.
5. [A1] 7.659 < σ ≤ 7.66 If M0 scored, SC B1 for 7.659 < σ < 7.66
6. [M1] {Both 1.5 and -1.5 seen as z-values or appropriate use of 1.5 or -1.5} and {no other z-values in part}.
7. [M1] Calculating the appropriate area from stated phis of z-values which must be ± the same number. Condone their 0.0668 as (1 – their 0.9332).
8. [A1] Accept answers wrt 0.866 If A0 scored SC B1 for answers wrt 0.866
9. [B1 FT] FT their 4SF (or better) probability, accept final answers to 3SF.