One day, garage A records the amount of petrol bought by the first 120 customers. The results are summarised in the table below. Petrol (k litres) | 0<k≤10 | 10<k≤20 | 20<k≤30 | 30<k≤40 | 40<k≤50 | 50<k≤60 | 60<k≤70 | 70<k≤80 ------------------|--------|----------|----------|----------|----------|----------|----------|---------- Number of customers | 9 | 13 | 36 | 30 | 16 | 9 | 5 | 2

1. (a)Complete the cumulative frequency table below. Petrol (k litres) | k≤10 | k≤20 | k≤30 | k≤40 | k≤50 | k≤60 | k≤70 | k≤80 ------------------|------|------|------|------|------|------|------|------ Cumulative frequency | 9 | 22 | | | | | | 120[1]
2. (b)On the grid below, draw a cumulative frequency curve to represent this data. [Figure 7.1][3]
3. (c)(i)Use your graph to estimate the median,[1]
4. (c)(ii)the 90th percentile of the distribution.[1]
5. (d)On the same day, garage B also recorded the amount of petrol bought by its first 120 customers. The results are summarised below. 6 customers bought 10 litres or less. The most petrol bought by any customer was 60 litres. The median amount of petrol bought was 34 litres. The lower quartile of the distribution was 25 litres. The interquartile range of the distribution was 19 litres. Draw the cumulative frequency curve for garage B on the grid on the previous page. [Figure 7.1][3]
6. (e)Petrol is priced at $2.60 per litre at both garages. Garage A offers a gift to customers who buy over 35 litres. Garage B offers a gift to customers who spend over $104. Use your graphs to estimate the number of these customers offered a gift at each garage and complete the sentence below. Answer Garage ............. offers a gift to ............. more customers than garage .........[3]

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