The times, in minutes, that Karli spends each day on social media are normally distributed with mean 125 and standard deviation 24.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.

1. [M1] Substitution of correct values into the Standardisation formula, allow continuity correction, not σ², √σ.
2. [M1] Appropriate numerical area Φ, from final process, must be probability, expect p < 0.5.
3. [A1] 0.239 < p < 0.240 to at least 3sf.
4. [M1 FT] their 4sf (or better) probability.
5. [A1 FT] Final answer must be positive integer, no indication of approximation/rounding, only dependent on previous M mark. SC B1 FT for their 3sf probability × 365 = integer value, condone 0.24 used.
6. [M1] One term: 10Cxp* (1 – p)10-x for 0 < x < 10, any p.
7. [A1 FT] Correct unsimplified expression using their probability to at least 3sf from (a)(i) or correct.
8. [A1] AWRT, WWW.
9. [B1] z = ±1.282 Correct value only, critical value.
10. [M1] Use of Standardisation formula with correct values substituted, allow continuity correction, σ², √σ, to form an equation with a z-value and not probability.
11. [A1] AWRT, condone AWRT 94.3. Not dependent on B mark.