The table below shows the distribution of the waiting times for some customers in a certain petrol station.
Waiting time (in mins)
No of customers
1.5 - 1.9
3
2.0 - 2.4
10
2.5 - 2.9
18
3.0 - 3.4
10
3.5 - 3.9
7
4.0 - 4.4
2
(a) Write down the class boundaries of the distribution. (b) Construct a cumulative frequency curve for the data; (c) Using your graph, estimate: (i) the interquartile range of the distribution ; (ii) the proportion of customers who could have waited for more than 3 minutes.
Explanation
Waiting time (in mins)
Class boundaries
No of customers
Cum Freq
1.5 - 1.9
1.45 - 1.95
3
3
2.0 - 2.4
1.95 - 2.45
10
13
2.5 - 2.9
2.45 - 2.95
18
31
3.0 - 3.4
2.95 - 3.45
10
41
3.5 - 3.9
3.45 - 3.95
7
48
4.0 - 4.4
3.95 - 4.45
2
50
(b) (c) Interquartile range of the distribution = From the graph, (ii) Proportion of customers who must have waited for more than 3 minutes =
