In the 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?

Transcribed Image Text:

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