For the 1,000-meter running event, Abby's mean time is 4.5 minutes with a standard deviation of 0.75 minutes. For the 800-meter event, Abby's mean time is 3.2 minutes with a standard deviation of 0.4 minutes. In the last track meet, Abby ran the 1,000-meter race in 4.1 minutes and the 800-meter race in 3 minutes. In which event did Abby have a better performance?

He performed better in the 800 m race

Step-by-step explanation:

Obtain the standardized score for each event :

Zscore = (score - mean) / standard deviation

1000 meter :

Mean = 4.5 ; Standard deviation = 0.75 ; x = 4.1

Zscore = (4.1 - 4.5) / 0.75

Zscore = - 0.4 / 0.75 = - 0.5333

800 meter :

Mean = 3.2 ; Standard deviation = 0.4 ; x = 3

Zscore = (3 - 3.2) / 0.4

Zscore = - 0.2 / 0.4 = - 0.5

-0.5 > - 0.533

Hence, he performed better in the 800 m race

Abby had a better performance in the 800-meter because this z-score was closer to the mean than the z-score for the 1,000-meter.

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