The weight, in grams, of pineapples is denoted by the random variable X which has a normal distribution with mean 500 and standard deviation 91.5. Pineapples weighing over 570 grams are classified as 'large'. Those weighing under 390 grams are classified as 'small' and the rest are classified as 'medium'.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.

1. [1] (i) Standardising for either 570 or 390, no cc, no sq, no √
2. [1] (i) One correct z value
3. [1] (i) One correct Φ, final solution
4. [1] (i) Correct small and large
5. [1] (i) Correct Medium rounding to 0.66 or ft 1 – (their small + their large)
6. [1] (ii) ± 1.645 seen (critical value)
7. [1] (ii) Standardising accept cc, sq, sq rt
8. [1] (ii) 650 < Ans < 651
9. [1] (iii) Attempt to find upper end prob x > 610 or Φ(x), ft their P(<390) from (i)
10. [1] (iii) Adding 0.3 to their P(x > 610) or subt 0.5 from Φ(x) or 0.8853 – 0.3
11. [1] (iii) Finding z = Φ⁻¹(0.5853)
12. [1] (iii) Standardising and solving, accept cc, sq, sqrt
13. [1] (iii) k = 520