Higher January 2022 Paper 1 Q12

EdexcelHigherCurrent spec6 marksCumulative Frequency

12 The table gives information about the times, in minutes, taken by 80 customers to do their shopping in a supermarket.

Time taken (\(t\) minutes)	Frequency
\(0 \lt t \leqslant 10\)	7
\(10 \lt t \leqslant 20\)	26
\(20 \lt t \leqslant 30\)	24
\(30 \lt t \leqslant 40\)	14
\(40 \lt t \leqslant 50\)	7
\(50 \lt t \leqslant 60\)	2

(a) Complete the cumulative frequency table. (1)

Time taken (\(t\) minutes)	Cumulative frequency
\(0 \lt t \leqslant 10\)
\(0 \lt t \leqslant 20\)
\(0 \lt t \leqslant 30\)
\(0 \lt t \leqslant 40\)
\(0 \lt t \leqslant 50\)
\(0 \lt t \leqslant 60\)

(b) On the grid below, draw a cumulative frequency graph for your table. (2)

A blank grid with cumulative frequency from 0 to 80 on the vertical axis and time taken in minutes from 0 to 60 on the horizontal axis

One of the 80 customers is chosen at random.

(d) Use your graph to find an estimate for the probability that the time taken by this customer was more than 42 minutes. (2)

Scheme	Marks
7, 33, 57, 71, 78, 80	B1
	(1)

Mark scheme (b)

Scheme	Marks
	B2
	(2)

Notes

B2: Fully correct cf graph – points at ends of intervals and joined with curve or line segments.
If not B2 then B1(ft from a table with only one arithmetic error) for 5 or 6 of their points at ends of intervals and joined with curve or line segments
OR for 5 or 6 points plotted correct at ends of intervals not joined OR for 5 or 6 points from table plotted consistently within each interval (not at upper ends of intervals) at their correct heights and joined with smooth curve or line segments.

Scheme	Marks
21 – 24	B1ft
	(1)

Mark scheme (d)

Scheme	Marks
	M1ft
\(\dfrac{8}{80}\)	A1ft
	(2)
	(6 marks)

Notes

M1ft: eg reading of 72 – 74 or 6 – 8
could be seen as the numerator of a fraction
ft their cf graph

A1ft: oe, ft their cf graph
fractional answers must have an integer numerator and denominator