The mean finish time for a yearly amateur auto race was 186.37 minutes with a standard deviation of 0.323 minute. the winning car, driven by ted , finished in 185.82 minutes. the previous year's race had a mean finishing time of 112.6 with a standard deviation of 0.141 minute. the winning car that year, driven by karen , finished in 112.25 minutes. find their respective z-scores. who had the more convincing victory?

Question

Mathematics

Ferguson

14 May, 20:20

The mean finish time for a yearly amateur auto race was 186.37 minutes with a standard deviation of 0.323 minute. the winning car, driven by ted , finished in 185.82 minutes. the previous year's race had a mean finishing time of 112.6 with a standard deviation of 0.141 minute. the winning car that year, driven by karen , finished in 112.25 minutes. find their respective z-scores. who had the more convincing victory?

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Ryleigh Sherman · Answer 1

The z-score is given by:

z = (x-μ) / σ

where:

μ-mean

σ - standard deviation

The z-score for ted will be:

x=185.82

μ=186.37

σ=0.323

thus

z = (186.37-185.82) / 0.323=1.70

The z-score for Karen:

x=112.25

μ=112.6

σ=0.141

hence:

z = (112.25-112.6) / 0.141=-2.48

Comparing the two z-score, we conclude that Ted had a convincing win because he has not deviated so much from the win.