Swimmer: Mean; SD Backstroke: 50.72; 0.24 Breaststroke: 55.51; 0.22 Butterfly: 4

Question

Swimmer: Mean; SD

Backstroke: 50.72; 0.24

Breaststroke: 55.51; 0.22

Butterfly: 49.43; 0.25

Freestyle: 44.91; 0.21

*Mean: 200.57

*SD: 0.461

a. What is the probability that the GREEN team’s total time will exceed 197 seconds

b. The team’s best total time so far this season is 199.48 seconds. What is the probability that the team will beat this best total time of 199.48 seconds, that is, swim in shorter time

c.Last year’s NCAA 400-YARD MEDLEY RELAY record is 179.22 seconds held by Texas. Do you think the GREEN team can beat this record? Explain in one sentence and justify using probability calculation

Explanation / Answer

Here mean swimming time for Green team's total swimming = 200.57 seconds

Standard deviation of total time for Green team's total swimming = 0.461 seconds

(a) If x is the total time for Green's team in a random event.

Pr(x > 197) = 1- NORM (x < 197 ; 200.57 ; 0.461)

Z = (197 - 200.57)/ 0.461 = -7.744

Pr(x > 197) = 1- NORM (x < 197 ; 200.57 ; 0.461) = 1- Pr(Z < -7.744) = 1 - 0 = 1

(b) Heere

Pr(x < 199.48 ; 200.57 ; 0.461)

Z = (199.48 - 200.57)/ 0.461 = -2.3644

Pr(x < 199.48 ; 200.57 ; 0.461) = Pr(Z < -2.3644) = 0.009

so there is only 0.009 probability that the team will beat this best total time of 199.48 seconds, that is, swim in shorter time

c. Here Pr(x < 179.22 ; 200.57 ; 0.461)

Z = (179.22 - 200.57)/ 0.461 = -46.31

so, Pr(z < -46.31) = 0.0000

so we can see that there is no probabiliry rha GREEN team can beat this record.

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