At a company’s call centre, 90% of callers are connected immediately to a representative. A random sample of 12 callers is chosen.

Mark scheme

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

1. [M1] One term ¹²Cx p^x (1-p)^(12-x), for 0 < x < 12, 0 < p < 1
2. [A1] Correct expression, accept unsimplified, no terms omitted, leading to final answer.
3. [B1] Mark the final answer at the most accurate value, 0.1108 < p < 0.111 WWW.
4. [M1] One term ¹²Cx p^x (1-p)^(12-x), for 0 < x < 12, 0 < p < 1
5. [A1] Correct expression, accept unsimplified, no terms omitted, leading to final answer. If answer correct condone omission of any 7 of the 8 middle terms.
6. [B1] Final answer 0.1108 < p < 0.111 WWW.
7. [B1] [Mean = 80 × 0.9 =] 72, [Variance = 80×0.9×0.1]=7.2 72 and 7.2 seen, allow unsimplified. May be seen in standardisation formula. (2.683 < σ < 2.684 imply correct variance).
8. [M1] Substituting their mean and √their variance into standardisation formula (any number for 69.5), not their 7.2, not √their 2.683
9. [M1] Using continuity correction 69.5 or 68.5 in their standardisation formula.
10. [M1] Appropriate area Φ, from final process, must be probability.
11. [A1] 0.8239 < p < 0.8243 WWW.
12. [B1] np=72, nq=8 Both greater than 5, [so approximation is valid] both np & nq referenced correctly. > 5 or greater than 5 seen.