The times taken (in seconds) by 120 athletes to complete a 400 m race are recorded below. The last class is open-ended.
Time (s)
50–55
55–60
60–65
65–70
70–75
75–80
80–85
85–90
90 and above
Frequency
8
12
18
24
22
17
9
6
4
(a) State a suitable upper class boundary for the last class so that the cumulative frequency curve can be drawn on a finite axis, and give a brief justification for your choice.
(b) Using the class boundaries decided in part (a), prepare the ‘less than’ cumulative frequency table.
(c) Draw the ‘less than’ cumulative frequency curve on graph paper, choosing convenient scales.
(d) From the curve, estimate the time below which 65 % of the athletes complete the race.