An elementary school class ran one mile with a mean of 12 minutes and a standard

Question

An elementary school class ran one mile with a mean of 12 minutes and a standard deviation of three minutes. Rachel, a student in the class, ran one mile in nine minutes. A junior high school class ran one mile with a mean of nine minutes and a standard deviation of two minutes. Kenji, a student in the class, ran 1 mile in 8.5 minutes. A high school class ran one mile with a mean of eight minutes and a standard deviation of four minutes. Nedda, a student in the class, ran one mile in ten minutes.

(a) Why is Kenji considered a better runner than Nedda, even though Nedda ran faster than he? (Round your standard deviations to two decimal places.)

Kenji is considered a better runner than Nedda because Kenji's time for one mile was ___ standard deviations faster than the mean of his class and Nedda's time was ___ standard deviations slowethan her class.

(b) Who is the fastest runner with respect to his or her class? Explain why. (Round your standard deviation to two decimal places.)

Rachel was the fastest runner with respect to his/her class as he/she had a time that was ___ standard deviation(s) faster than his/her class.

Explanation / Answer

as zscore =(X-mean)/std deviation

here z score for Rachel =(9-12)/3=-1

here z score for Kenji =(8.5-9)/2=-0.25

here z score for Nedda =(10-8)/4=0.5

a)Kenji is considered a better runner than Nedda because Kenji's time for one mile was 0.25 standard deviations faster than the mean of his class and Nedda's time was 2 standard deviations slowethan her class

b)Rachel was the fastest runner with respect to his/her class as he/she had a time that was 1 standard deviation(s) faster than his/her class.

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