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In: Statistics and Probability

In the 4x100 medley relay event in swimming, four swimmers swim 100 yards, each using a...

In the 4x100 medley relay event in swimming, four swimmers swim 100 yards, each using a different stroke. The four medley relay swimmers for a college team preparing for their conference championships have the following summary statistics (in seconds) for the four strokes:

1(backstroke) - Expected Value = 49 ; Stand. Dev = 0.34

2(breaststroke) - Expected Value = 54.76 ; Stand. Dev = 0.34

3(butterfly) - Expected Value = 48.5 ; Stand. Dev. = 0.21

4(freestyle - Expected Value = 45.28 ; Stand. Dev. 0.28

Let the random variable T denote the relay team's total time in the medley event. Determine the standard deviation SD(T) (use 3 decimal places).

Please show work on how to get variance.

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