Mathematics (AS & A Level) · Oct / Nov 2016 · Paper 73 · Question 3
9709
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A men’s triathlon consists of three parts: swimming, cycling and running. Competitors’ times, in minutes, for the three parts can be modelled by three independent normal variables with means 34.0, 87.1 and 56.9, and standard deviations 3.2, 4.1 and 3.8, respectively. For each competitor, the total of his three times is called the race time. Find the probability that the mean race time of a random sample of 15 competitors is less than 175 minutes. [5]
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