Linda Laces and Mary Thon are trying to qualify for the Camptown Races. Runners

Question

Linda Laces and Mary Thon are trying to qualify for the Camptown Races. Runners may pick one of two options for qualification (and may not change their mind once they choose an option):

1. Select one marathon, and run the marathon in under three hours.

2. Select three marathons, and run an average marathon time of under three hours. Assume that each marathon time is independent of others.

Let Z N(, 2) denote a normal random variable Z with mean and variance 2. Linda has a marathon running time distribution of L N(2.8, 1), and Mary has a running time distribution of M N(3.2, 1), both measured in hours. Provide a quantitative argument to determine which of the twos options each of these runners should choose to maximize their probability of qualifying.

Explanation / Answer

In this case we have to caluculate Coeffiecient of variation(CV) which is used comare any two or more distributions

Decision : If CV is less value then it is considered as better than any other distribution

CV for Linda = [sd/mean]*100 = [1/2.8]*100 = 35.71%

CV for Marathon = [sd/mean]*100 = [1/3.2]*100 = 31.25%

In this problem, Marathon choose to maximize his probability of qualifying

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