Question

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?

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.