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Answer:
Devon has the lower z-score, so he ran the mile faster relative to his gender.
Step-by-step explanation:
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Who ran the mile faster relative to their gender?
The lower the percentile of time ran, the faster. So whoever has the lower z-score ran the mile faster.
Devon
His best time to run the mile is 6.6 minutes.
These times are approximately normal with mean 8 minutes and standard deviation 1 minute.
We have to find Z when . So
Kendall
Her best time to run the mile is 5.7 minutes.
These times are approximately normal with mean 7.5 minutes and standard deviation 2 minutes.
We have to find Z when . So
Devon has the lower z-score, so he ran the mile faster relative to his gender.