The lengths of the rods produced by a company are normally distributed with mean 55.6mm and standard deviation 1.2 mm.

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 54.8, 55.6 and 1.2 substituted. condone 1.2², √1.2 or continuity correction of 54.75 or 54.85
2. [M1] Appropriate area Φ, from final process, must be probability.
3. [A1] 0.252 < p < 0.2525 If A0 scored SC B1 for 0.252 < p < 0.2525
4. [B1 FT] FT their 4SF (or better) probability from a normal calculation. Must be a single integer answer.
5. [M1] {Both ½ and –½ seen as z-values or appropriate use of +½ or -½} and {no other z-values in part}. Condone 56.2-55.6 / 1.2 and 55[.0]-55.6 / 1.2 seen as z-values.
6. [M1] Calculating the appropriate area from stated phis of z-values which must be the same number.
7. [A1] 0.3829 < z < 0.383 If A0 scored SC B1 for 0.3829 < z < 0.383