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. Miles run in 30 minutes 2 a 4 4.5 5.7 a) Find the value of a. [2 marks] b) The distance in miles, M, can be converted to the distance in kilometres, K, using the formula K = 8/5 M. Write down the value of the median distance in kilometres (km). [1 mark] c) The variance of the distances run by the athletes is 16/9 km^2. The standard deviation of the distances is b miles. Find the value of b. [4 marks] 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. 600 500 400 300 200 100 0 10 20 30 40 50 time (minutes) There were 400 athletes who took between 22 and m minutes to complete the 5 km race. d) Find m. [3 marks] The first 150 athletes that completed the race won a prize. e) 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 marks]
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