The cumulative frequency graph shows the speeds, in miles per hour (mph), of vehicles passing a 40 mph speed limit sign on a road - OCR - GCSE Maths - Question 12 - 2017 - Paper 1

To find the total number of vehicles, we note that the cumulative frequency at the maximum speed observed (50 mph) is 80. Hence, the total number of vehicles is 80.

Now, we calculate the percentage of vehicles exceeding the speed limit of 40 mph. This can be done using the formula:

$ext{Percentage} = \left( \frac{\text{Cumulative frequency at 40 mph}}{\text{Total vehicles}} \right) \times 100$

Substituting the values, we get:

$\text{Percentage} = \left( \frac{55}{80} \right) \times 100 = 68.75\%$

Since 68.75% of vehicles are above the speed limit of 40 mph, which is greater than 30%, a speed camera should indeed be installed.