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 here.

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

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?