H1 maths statistics

11 The times taken, in minutes, for runners from two large athletics clubs, the Arrows and the Beavers, to run 5000 metres have independent normal distributions with means and standard deviations as shown in the following table. Mean Standard Deviation Arrows 14.8 0.55 Beavers 15.2 0.65 (i) Find the probability that the time taken to run 5000 metres by a randomly chosen runner from the Arrows is more than 15.0 minutes. [1] (ii) Find the probability that the sum of the times taken by 2 randomly chosen runners from the Arrows and 3 randomly chosen runners from the Beavers is less than 75 minutes. [4] In a competition, teams of 6 runners enter a 5000-metre race. The score for each team is the sum of the times taken, in minutes, by the 6 runners to complete the race. The team with the lowest score wins the competition. The Arrows and the Beavers each enter a team of 6 randomly chosen runners from their clubs. (iii) Find the probability that the score of the Arrows team is within 15 of the score of the Beavers team. [4] Any team that scores fewer than 90 wins a medal. (iv) Find the probability that neither the Arrows nor the Beavers win a medal. [4