4MA0 Higher June 2017 Paper 3 Q11

EdexcelHigherOld spec7 marksBasic ProbabilityCumulative Frequency

11 The table gives information about the ages of all the 90 adults in a supermarket.

Age (\(t\) years)Frequency
\(20 \lt t \leqslant 30\)4
\(30 \lt t \leqslant 40\)28
\(40 \lt t \leqslant 50\)30
\(50 \lt t \leqslant 60\)16
\(60 \lt t \leqslant 70\)8
\(70 \lt t \leqslant 80\)4

One of these 90 adults is picked at random.

(a) Find the probability that this adult's age is more than 50 years. (2)
(b) Complete the cumulative frequency table for these 90 adults.
Age (\(t\) years)Cumulative frequency
\(20 \lt t \leqslant 30\)
\(20 \lt t \leqslant 40\)
\(20 \lt t \leqslant 50\)
\(20 \lt t \leqslant 60\)
\(20 \lt t \leqslant 70\)
\(20 \lt t \leqslant 80\)
(1)
(c) On the grid, draw a cumulative frequency graph for your table.
Grid with cumulative frequency from 0 to 90 on the vertical axis and age (t years) from 20 to 80 on the horizontal axis
(2)

All of these adults with an age greater than 65 years receive a discount on their shopping bill.

(d) Use your graph to find an estimate for the number of these adults who receive a discount. (2)
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