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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:

Swimmer Mean St. Dev.
1 (backstroke) 50.72 0.22
2 (breaststroke) 55.51 0.16
3 (butterfly) 49.43 0.3
4 (freestyle) 44.91 0.24


Question. Let the random variable T denote the relay team's total time in the medley event. Determine the mean E(T) and standard deviation SD(T).

Respuesta :

Chrisnando

Answer:

E(T) = 200.57

SD(T) = 0.4625

Step-by-step explanation:

a) Given:

Mean:

Backstroke = 50.72

Breaststroke = 55.51

Butterfly = 49.43

Freestyle = 44.91

To find the mean E(T), let's sum up all values of mean.

E(T) = 50.75 + 55.31 + 49.43 + 44.91

E(T) = 200.57

b) Given:

Standard deviation :

Backstroke = 0.22

Breaststroke = 0.16

Butterfly = 0.3

Freestyle = 0.24

To get the SD(T), let's first find their variance.

Variance = SD²

Therefore,

Vbackstroke = 0.22² = 0.0484

Vbreatstroke= 0.16² = 0.0256

Vbutterfly = 0.3² = 0.09

Vfreestyle = 0.24² = 0.0576

[tex] SD(T) = \sqrt{0.0484 + 0.0256 + 0.09 + 0.0576} [/tex]

SD(T) = 0.4625

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