An athlete who is training for a marathon aims to complete many laps of a running track while running at a constant speed. In practice, the athlete’s judgement of pace is not perfect, and the time taken to complete a randomly chosen lap may be taken to be normally distributed with a mean of 65 seconds and standard deviation of 0.8 second. The time taken for any lap may be assumed to be independent of the time taken for any other lap. (a) What is the probability that a randomly chosen lap will take more than 64 seconds? (b) What is the probability that each of three randomly chosen laps will take more than 64 seconds? (c) The probability that the athlete will complete a randomly chosen lap in less than x seconds is 0.99. Find x
An athlete who is training for a marathon aims to complete many laps of a running track while running at a constant speed. In practice, the athlete’s judgement of pace is not perfect, and the time taken to complete a randomly chosen lap may be taken to be
(a) What is the probability that a randomly chosen lap will take more than 64 seconds?
(b) What is the probability that each of three randomly chosen laps will take more than 64 seconds?
(c) The probability that the athlete will complete a randomly chosen lap in less than x seconds is 0.99. Find x.
(d) What is the probability that exactly one out of 50 randomly chosen laps will take more than x seconds?
(e) What is the probability that the average time for three randomly chosen laps will be less than 1 minute and 4 seconds?
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