In: Statistics and Probability
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.