2020 NOV Afternoon P1 Q8

Each athlete on a running team recorded the distance (\(M\) miles) they ran in \(30\) minutes.
The median distance is \(4\) miles and the interquartile range is \(1.1\) miles.
This information is shown in the following box-and-whisker plot.

1. Find the value of \(a\).

   [2]

The distance in miles, \(M\), can be converted to the distance in kilometres, \(K\), using the formula \(K = \frac{8}{5}M\).

2. Write down the value o f the median distance in kilometres (km).

   [1]

The variance of the distances run by the athletes is \(\frac{16}{9}\) km\(^2\).
The standard deviation of the distances is \(b\) miles.

3. Find the value of \(b\).

   [4]

A total of \(600\) athletes from different teams compete in a \(5\)km race. The times the \(600\) athletes took to run the \(5\) km race are shown in the following cumulative frequency graph.

There were \(400\) athletes who took between \(22\) and \(m\) minutes to complete the \(5\) km race.

4. Find \(m\).

   [3]

The first \(150\) athletes that completed the race won a prize.

5. Given that an athlete took between \(22\) and \(m\) minutes to complete the \(5\) km race, calculate the probability that they won a prize.

   [5]