0580 P42 - Jun 2020 - Q3 - 16 marks
13297
The speed v km/h of 200 cars is measured.
| Speed | \(0<v\le20\) | \(20<v\le40\) | \(40<v\le45\) | \(45<v\le50\) | \(50<v\le60\) | \(60<v\le80\) |
|---|---|---|---|---|---|---|
| Frequency | 16 | 34 | 62 | 58 | 26 | 4 |
(a) Estimate the mean speed. [4]
(b(i)) Complete the cumulative frequency table.
| Speed | \(v\le20\) | \(v\le40\) | \(v\le45\) | \(v\le50\) | \(v\le60\) | \(v\le80\) |
|---|---|---|---|---|---|---|
| Cumulative frequency | 16 | 50 | … | … | 196 | 200 |
(b(ii)) Draw a cumulative frequency diagram. [3]
(b(iii)(a)) Use the diagram to estimate the upper quartile. [1]
(b(iii)(b)) Use the diagram to estimate how many cars have speed greater than 35 km/h. [2]
(c) Choose two of the 200 cars randomly without replacement. Find the probability both have speed greater than 50 km/h. [2]
(d) Draw a histogram for the combined intervals.
| Speed | \(0<v\le40\) | \(40<v\le50\) | \(50<v\le80\) |
|---|---|---|---|
| Frequency | 50 | 120 | 30 |
