O-LevelMathematicsStatistics4024/22 · Oct/Nov 2020 · Q211 Marks

(a) A group of 80 students each completed a task. The table shows the time, t minutes, each student took to complete the task. Time (t minutes) | 20 < t ≤ 40 | 40 < t ≤ 60 | 60 < t ≤ 80 | 80 < t ≤ 100 | 100 < t ≤ 120 -----------------|-------------|-------------|-------------|---------------|---------------- Frequency | 10 | 20 | 34 | 12 | 4

(a)(i)On the grid, draw a cumulative frequency diagram to represent this information. [Grid with axes labeled Cumulative frequency and Time (minutes)][3]
(a)(ii)(a)the median,[1]
(a)(ii)(b)the interquartile range.[2]
(b)(i)Calculate the mean.[2]
(b)(ii)One of the adults is selected at random. Find the probability that this adult made more than 3 errors.[1]
(b)(iii)Two of the adults are selected at random. Find the probability that they each made exactly one error.[2]

This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.

[3] B2 for at least 4 correct points plotted; or B1 for 10, 30, 64, 76, 80 soi; Correct smooth curve drawn.
[1] Correct reading at CF of 40 from their cumulative frequency diagram.
[2] FT their cumulative frequency diagram; B1FT for correct reading of their LQ or their UQ; Final answer 24 to 28.
[2] M1 for ([0 × 24] + 1 × 30 + 2 × 50 + 3 × 32 + 4 × 16 + 5 × 8) ÷ 160; Final answer 2.0625 or 2.063 or 2 1/16.
[1] (16 + 8) / 160 or 24/160 oe.
[2] M1 for 30/160 * 29/159 oe; Final answer 29/848 oe.

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