Mean and standard deviation for the relay team

Reference no: EM131008669

1. For a new type of tire, a NASCAR team found the av- erage distance a set of tires would run during a race is 168 miles, with a standard deviation of 14 miles. Assume that tire mileage is independent and follows a Normal model.

a) If the team plans to change tires twice during a 500-mile race, what is the expected value and standard deviation of miles remaining after two changes?

b) What is the probability they won't have to change tires a third time before the end of a 500-mile race?

2. In the 4 * 100 medley relay event, four swimmers swim 100 yards, each using a different stroke. A college team preparing for the conference championship looks at the times their swimmers have posted and creates a model based on the following assumptions:

The swimmers' performances are independent.
Each swimmer's times follow a Normal model.
The means and standard deviations of the times (in sec- onds) are as shown here.

Swimmer	Mean	SD
1 (backstroke)	50.72	0.24
2 (breaststroke)	55.51	0.22
3 (butterfly)	49.43	0.25
4 (freestyle)	44.91	0.21

a) What are the mean and standard deviation for the relay team's total time in this event?

b) The team's best time so far this season was 3:19.48. (That's 199.48 seconds.) What is the probability that they will beat that time in the next event?

Reference no: EM131008669

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