Question

The mean on a Advanced Algebra test was 86 with a standard deviation of 4.5. If the test scores are normal distributed, find the interval about the mean that contains 68% of the scores. Use the empirical rule.

Answer 1

Using the Empirical Rule, the interval that contains 68% of the scores is [81.5, 90.5].

What does the Empirical Rule state?

It states that, for a normally distributed random variable:

• Approximately 68% of the measures are within 1 standard deviation of the mean.

• Approximately 95% of the measures are within 2 standard deviations of  the mean.

• Approximately 99.7% of the measures are within 3 standard deviations of the mean.

68% of the scores are within 1 standard deviation of the mean, hence the bounds of the interval are:

• 86 - 4.5 = 81.5.

• 86 + 4.5 = 90.5.

More can be learned about Empirical Rule at brainly.com/question/24537145

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