Mathematics, 18.01.2021 14:00 TheOriginal2x

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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Answer from: Kyliehayden05

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 $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

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 $X = 8.5, \mu = 9, \sigma = 2$ . So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{8.5 - 9}{2}$

Z = -0.25

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 $X = 8, \mu = 7, \sigma = 4$ . So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{8 - 7}{4}$

Z = 0.25

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 $X = 7, \mu = 12, \sigma = 3$

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{7 - 12}{3}$

Z = -1.67

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

Answer from: Quest

There is no association.
Which statement best describes the association between variable x and variable y? perfect negative

Answer from: Quest

b if for most of the graph

d if y intercept

step-by-step explanation:

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