The lengths, in cm, of the leaves of a particular type are modelled by the distribution N(5.2, 1.5²).

Mark scheme

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

1. [M1] 6, 5.2, 1.5 substituted into z standardisation formula, condone 1.5^2, continuity correction ±0.5
2. [A1] 0.703
3. [B1] 1.328 < z1 < 1.329 or -1.329 < z1 < -1.328
4. [B1] 0.877 < z2 < 0.878 or -0.878 < z2 < -0.877
5. [M1] Use of the z standardisation formula once with μ, σ, a z-value (not 0.8179, 0.7910, 0.5367, 0.5753, 0.19, 0.092 etc.) and 3 or 8, condone continuity correction but not σ² or √σ
6. [M1] Use either the elimination method or the substitution method to solve their two equations in μ and σ
7. [A1] 2.26 < σ <= 2.27, 6.01 < μ <= 6.02
8. [M1] Identify 1 and -1 as the appropriate z-values.
9. [M1] Calculating the appropriate area from stated phis of z-values which must be ± the same number
10. [A1] Accept AWRT 0.317
11. [B1 FT] FT their 4 s.f. (or better) probability, final answer must be positive integer no approximation or rounding stated