The heights of the members of a club are normally distributed with mean 166cm and standard deviation 10cm. Find the probability that a randomly chosen member of the club has height less than 170cm.

Mark scheme

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

1. [M1] Use of ± standardisation formula with 170, 166 and 10 substituted appropriately, condone 10², √10, condone continuity correction ±0.5.
2. [A1] 0.655 (0.655 < p < 0.6555). If M0 awarded, SC B1 for correct answer www.
3. [B1] 0.253 (0.253 ≤ z < 0.2535 or -0.2535 < z < -0.253) seen.
4. [M1] Use of the standardisation formula with h, 166, 10 and a z-value (not 1 – z-value), not 10², √10, no continuity correction.
5. [A1] 168.53 (168.53 < h < 168.535, 168.5). If M0 scored, SC B1 for 168.53 < h < 168.535, 168.5. SC B1 for 168.54 from z = 0.254.
6. [M1] Use of the standardisation formula with 0, μ and 2/3 μ substituted for σ. Or use of the standardisation formula with 0, σ and -3/2 σ substituted for μ.
7. [A1] -1.5 seen, no additional terms (e.g. x – 1.5 A0). Condone Z < 1.5. If M0 scored, SC B1 Z > -1.5 or Z < -1.5 seen www.
8. [A1] 0.933 (0.933 < p < 0.9333). If M0 scored, SC B1 0.933 < p < 0.9333 seen www.