Complete question :
Swim team Hanover High School has the best women’s swimming team in the region. The 400- meter freestyle relay team is undefeated this year. In the 400-meter freestyle relay, each swimmer swims 100 meters. The times, in seconds, for the four swimmers this season are approximately Normally distributed with means and standard deviations as shown. Assuming that the swimmer’s individual times are independent, find the probability that the total team time in the 400-meter freestyle relay is less than 220 seconds. Follow the four-step process
Answer:
0.225
Step-by-step explanation:
Given the data:
Swimmer__ Mean __Std. dev.
Wendy ___ 55.2 ____ 2.8
Jill _______ 58.0 ____ 3.0
Carmen____56.3 ____ 2.6
Latrice_____54.7_____2.7
Team average = (55.2 + 58 + 56.3 + 54.7) = 224.2
Team standard deviation = (2.8 + 3 + 2.6 + 2.7) = 11.1
Standard Error = 11.1 /sqrt(n)
Standard Error = 11.1 / sqrt(4)
Standard Error (S. E) = 11.1 / 2 = 5.55
P(x < 220) :
(x - mean) / S.E
(220 - 224.2) / 5.55
= −0.756756
P(Z < - 0.757) = 0.22452
P(Z < - 0.757) = 0.225
