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 seconds) are as shown:

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.) Do you think the team is likely to swim faster than this at the conference championship? Explain.

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