4. There are 4 runners on the New High School team. The team is planning to participate in a race in which each runner runs a mile. The team time is the sum of the individual times for the 4 runners. Assume that the individual times of the 4 runners are all independent of each other. The individual times, in minutes, of the runners in similar races are approximately normally distributed with the following means and standard deviations. Standard Mean Deviation Runner I 4.9 0.15 Runner 2 4.7 0.16 Runner 3 4.5 0:14 Runner 4 4.8 0.15 a) Runner 3 thinks he can run a mile in less than 4.2 minutes in the next race. Is this likely to happen? Explain. 4.2-4.5 P(z< = 0. 0.14 No berase ther's oNy 1.6% chaue of thet b) The distribution of team times is approximately normał. What are the mean and standard devia- tion of this distribution? M=20-0.1-0.3- 0.3-0.2=10.9 0.1S ) Suppose the team's best time to date is I8.4 minutes. What is the probability that the team will beat its best time in the next race? Vale P(Z> 18.4-18.9 0. 3003 = 0,048

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