In the 4 X 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 seconds) are as shown here.

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?

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