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2 June, 11:33

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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  1. 2 June, 11:44
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    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.
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