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?

Ted had a more convincing victory with about 4.46%

The z score is used to determine by how many standard deviations the raw score is above or below the mean.

The z score is given by:

For ted, μ = 186.37 minutes , σ = 0.323

For x < 185.82 minutes:

From the normal distribution table, P(z < -1.70) = 0.0446 = 4.46%

For karen, μ = 112.6 minutes , σ = 0.141

For x < 112.25 minutes:

From the normal distribution table, P(z < -2.48) = 0.0066 = 0.6%

Hence Ted had a more convincing victory with about 4.46%

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