The weights of apples sold by a store can be modelled by a normal distribution with mean 120 grams and standard deviation 24 grams. Apples weighing less than 90 grams are graded as 'small'; apples weighing more than 140 grams are graded as 'large'; the remainder are graded as 'medium'.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.

1. [M1] At least one standardisation, no cc, no sq rt, no sq using 120 and 24 and either 90 or 140
2. [A1] -5/4 and 5/6 unsimplified
3. [M1] Correct area Φ – Φ legitimately obtained and evaluated from phi(their z2) - phi (their z1)
4. [A1] Correct answer obtained from 0.7975 and 0.1056 oe to 4sf or 0.6919 seen www
5. [M1] Any binomial term of form 4Cxp^x (1-p)^(4-x), x ≠ 0 or 4 (Method 1)
6. [B1] One correct bin term with n=4 and p=0.692, (Method 1)
7. [M1] Correct unsimplified expression using 0.692 or better (Method 1)
8. [A1] Correct answer (0.910) (Method 1)
9. [M1] Any binomial term of form 4Cxp^x (1-p)^(4-x), x≠0 or 4 (Method 2)
10. [B1] One correct bin term with n = 4 and p = 0.692 (Method 2)
11. [M1] Correct unsimplified expression using 0.692 or better (Method 2)
12. [A1] Correct answer (0.910) (Method 2)