Kuya participated in 10-K races held in several states. He provided you with the
ID: 3353525 • Letter: K
Question
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 8Explanation / Answer
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.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.