O-LevelMathematicsStatistics4024/22 · Oct/Nov 2015 · Q1012 Marks

The length of time taken by 80 drivers to complete a particular journey is summarised in the table below.

(a)Using a scale of 2 cm to represent 10 minutes, draw a horizontal axis for times from 60 minutes to 130 minutes. Choose a suitable scale for the vertical axis and draw a histogram to represent this information.[3]
(b)In which of the intervals does the median time lie?[1]
(c)Calculate an estimate of the mean time taken to complete the journey.[3]
(d)One driver is chosen at random. Calculate the probability that this driver took 95 minutes or less for the journey.[1]
(e)(i)Two of the 80 drivers are chosen at random. Calculate the probability that both took more than 100 minutes for the journey.[2]
(e)(ii)Calculate the probability that one took 80 minutes or less and the other took more than 110 minutes.[2]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2015). The mark or mark type is shown in brackets.

[3] If 3 not scored, up to 2 marks from: B1 for correct fd's (allow one error) B1 for correct column widths B1 for correct heights from their fd's
Correct histogram
[1] 95 < t ≤ 100
[3] M1 for Σfx B1 for division by 80 seen
98.2
[1] 28/80 oe
[2] M1 for 32/80 × 31/79 or 32/80 × 32/80
992/6320 oe
[2] M1 for 4/80 × 8/79 or 2x 4/80 × 8/80
64/6320 oe

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