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Many soccer players have high levels of stamina and can run long distances. The mean distance they can travel in a match is 10km. Suppose the standard deviation is 5 and 28 players are selected at random.
a) What is the probability that the mean distance for the 28 players will be less than 8km?
b) What is the probability that the mean distance for the 28 players will be between 9.5km and 10.5km?
c) During training the coach worked on leg power to improve their distance running. After a few months of training, the mean distance ran for 40 of these players selected at random was 11.5km. Is there evidence to suggest that the leg power training increased the mean distance of the players, mean = 10km.
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