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## 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,

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 seven 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 seven minutes and a standard deviation of four minutes. Nedda, a student in the class, ran one mile in eight minutes.

Required:

a. Why is Kenji considered a better runner than Nedda, even though Nedda ran faster than he?

b. Who is the fastest runner with respect to his or her class? Explain why.

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Mathematics
3 years
2021-08-18T00:14:30+00:00
2021-08-18T00:14:30+00:00 1 Answers
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## Answers ( )

Answer:a)Since Kenji’s time has a lower Z-score’s than Nedda, he is considered a better runner relative to his competition.b)Since her time has the lowest Z-score, Rachel is the fastest runner with respect to her class.Step-by-step explanation:Z-score: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.

a. Why is Kenji considered a better runner than Nedda, even though Nedda ran faster than he?We have to see their z-scores.

Whoever has the lower z-score is in the lower percentile of times, that is, runs faster.

Kenji: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.

So Kenji’s z-score is found when . So

Nedda:A high school class ran one mile with a mean of seven minutes and a standard deviation of four minutes. Nedda, a student in the class, ran one mile in eight minutes.

So Nedda’s z-score is found when . So

Since Kenji’s time has a lower Z-score’s than Nedda, he is considered a better runner relative to his competition.

b. Who is the fastest runner with respect to his or her class? Explain why.Whoever has the lower z-score.

We have the z-scores for Kenji and Nedda, and we have to find

Rachel’s z-score.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 seven minutes.

So Rachel’s z-score is found when

Since her time has the lowest Z-score, Rachel is the fastest runner with respect to her class.