Question

In a relay event, four swimmers swim 100 yards, each using a different stroke. A college team looks at the times Mean SD p Swimmer 1 (backstroke) 50.08 0.21 for the swimmers and creates a model based on the 2 (breaststroke) 54.97 0.18 assumptions that the swimmers' performances are independent, each swimmer's times follow a normal model, and the means and standard deviations of the times in seconds are as shown in the table. 3 (butterfly) 48.51 0.24 4 (freestyle) 44.52 0.23 a) What are the mean and the standard deviation for the relay team's total time in this event? μ= (Round to two decimal places as needed.) b) The team's best time so far this season was 3:17.80 (which is 197.80 seconds). Do you think the team is likely to swim faster than this at the conference championship? Explain. O A. Yes, because the chance of beating their best is less than 5%. O B. No, because chance of beating their be O C. No, because the chance of beating their best is less than 5%. O D. Yes, because the chance of beating their best is more than 5%. is more

Answer 1

a Mean total fime Standand douiation 198.08 nelonds 2 randorn variable 0.4324 0.43 1 P(Z 197.8-198.08 Or4324 1- P(Z-0645) P(Z>-0-64子S) b) P(x>1978) 11 1 O.O5 0イ4135 D Yes, belause the chante of beating their best iu moe than s%. So, yes they Can m faster Han theis bext time