# Math215 – Statistical Concepts Z-Scores Worksheet 2016

Question

Z-Scores Worksheet

Group 1

1. Consider an infinite population with a normal shape and a mean of 250 and standard deviation of 30.

a. Draw the distribution on the curve below including values in the scale for one, two, and three standard deviations from the mean.

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b. Compute the z-scores for the following values of X and locate each on the graph.

X

Z-score

200

320

220

270

250

c. According to the Empirical rule, what percent of the data should be between 220 and 280? Between 190 and 310?

d. According to Chebyshev, what percent should be between 200 and 300?

e. Why is the z-score of the mean zero?

f. A student scores 34 on an English test that has a mean of 28 and a standard deviation of 5. He scores a 28 on a math test that has a mean of 25 and a standard deviation of 2. Which score is higher and why?

Group 2:

2. Consider an infinite population with a normal shape and a mean of 500 and standard deviation of 100.

a. Draw the distribution on the curve below including values in the scale for one, two, and three standard deviations from the mean.

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b. Compute the z-scores for the following values of X and locate each on the graph.

X

Z-score

800

350

620

500

250

c. According to the Empirical rule, what percent of the data should be between 400 and 600? Between 300 and 700?

d. According to Chebyshev, what percent should be between 250 and 750?

e. Why is the z-score of the mean zero?

f. A student scores 31 on an English test that has a mean of 28 and a standard deviation of 5. He scores a 28 on a math test that has a mean of 25 and a standard deviation of 7. Which score is higher and why?

Group 3

3. Consider an infinite population with a normal shape and a mean of 80 and standard deviation of 16.

a. Draw the distribution on the curve below including values in the scale for one, two, and three standard deviations from the mean.

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b. Compute the z-scores for the following values of X and locate each on the graph.

X

Z-score

100

56

80

72

85

c. According to the Empirical rule, what percent of the data should be between 64 and 96? Between 48 and 112?

d. According to Chebyshev, what percent should be between 56 and 104?

e. Why is the z-score of the mean zero?

f. A student scores 36 on an English test that has a mean of 28 and a standard deviation of 5. He scores a 29 on a math test that has a mean of 25 and a standard deviation of 2. Which score is higher and why?

Group 4

4. Consider an infinite population with a normal shape and a mean of 250 and standard deviation of 60.

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b. Compute the z-scores for the following values of X and locate each on the graph.

X

Z-score

100

320

420

250

190

c. According to the Empirical rule, what percent of the data should be between 190 and 310? Between 130 and 370?

d. According to Chebyshev, what percent should be between 130 and 370?

e. Why is the z-score of the mean zero?

f. A student scores 34 on an English test that has a mean of 28 and a standard deviation of 10. He scores a 28 on a math test that has a mean of 25 and a standard deviation of 3. Which score is higher and why?

Group 5

5. Consider an infinite population with a normal shape and a mean of 300 and standard deviation of 30.

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b. Compute the z-scores for the following values of X and locate each on the graph.

X

Z-score

200

360

220

270

300

c. According to the Empirical rule, what percent of the data should be between 270 and 330? Between 240 and 360?

d. According to Chebyshev, what percent should be between 240 and 360?

e. Why is the z-score of the mean zero?

f. A student scores 33 on an English test that has a mean of 28 and a standard deviation of 5. He scores a 27 on a math test that has a mean of 25 and a standard deviation of 2. Which score is higher and why?

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