Question: Medley. 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:
Swimmer Mean SD
1 (backstroke) 50.72 0.24
2 (breadstroke) 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.) Do you think the team is likely to swim faster than this at the conference championship? Explain.