# Chebyshev: Normal Populations and testing

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

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

X Z-score

200

360

220

270

300

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

c. According to Chebyshev what percent should be between 240 and 360

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

e. A student scores 33 on and 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?

3.

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

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

X Z-score

100

56

80

72

85

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

C According to Chebyshev what percent should be between 56 and 104

D Why is the z-score of the mean zero?

E A student scores 36 on and 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?

See attached file for full problem description.

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The solution tests some normally distributed statistics.