Question

In: Statistics and Probability

Kuya participated in 10-K races held in several states. He provided you with the times completed...

Kuya participated in 10-K races held in several states. He provided you with the times completed by each runner. Which state did he do best and which state the worst in comparison to the group of runners for that state?

Georgia

Maine

Nevada

Ohio

Texas

	Georgia	Maine	Nevada	Ohio	Texas
Runner 1	3	6	4	4	5
Runner 2	5	5	6	6	6
Runner 3	3	7	5	3	4
Runner 4	4	8	7	5	7
Runner 5	6	7	6	4	7
Runner 6	5	4	7	3	6
Kuya	4	5	5	4	5
Runner 8	6	6	6	6	7
Runner 9	4	5	8	3	3
Runner 10	3	8	7	4	7
Runner 11	5	6	3	3	6
Runner 12	4	7	4	5	2
Runner 13	3	6	5	4	5
Runner 14	4	8	4	6	7
Runner 15	6	2	6	3	6
Runner 16	6	7	4	2	8

Expert Solution

The average and standard deviation of time completed by each runner at each state is,

Georgia - mean = 4.4375 , sd = 1.152895

Maine - mean = 6.0625, sd = 1.611159

Nevada - mean = 5.4375, sd = 1.41274

Ohio - mean = 4.0625, sd = 1.236595

Texas - mean = 5.6875, sd = 1.621471

Caculating z-score of Kuya time for each state,

Georgia - z = (4 - 4.4375)/ 1.152895 = -0.3795

Maine - z = (5 - 6.0625) / 1.611159 = -0.6595

Nevada - z = (5 - 5.4375) / 1.41274 = -0.3097

Ohio - z = (4 - 4.0625) / 1.236595 = -0.0505

Texas - z = (5-5.6875)/1.621471 = -0.424

The most negative valus is for Maine, (z = -0.6595), which means that Kuya time was far less than the average time of the other runners.

The least negative valus is for Ohio, (z = -0.0505), which means that Kuya time was near than the average time of the other runners.

Thus, Kuya's best performance was in Maine and worst performance was in Ohio.

orchestra answered 2 years ago

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