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The mean score of a competency test is 73, with a standard deviation of 4. Use the Empirical Rule to find the percentage of scores between 69 and 77. (Assume the data set has a bell-shaped distribution.)

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Final answer:

The Empirical Rule states that for data that follows a bell-shaped distribution, approximately 68% of the data falls within one standard deviation of the mean, about 95% falls within two standard deviations, and more than 99% falls within three standard deviations. In this case, the mean score is 73 and the standard deviation is 4. The percentage of scores between 69 and 77 is approximately 68%.

Step-by-step explanation:

The Empirical Rule states that for data that follows a bell-shaped distribution, approximately 68% of the data falls within one standard deviation of the mean, about 95% falls within two standard deviations, and more than 99% falls within three standard deviations.

In this case, the mean score is 73 and the standard deviation is 4. To find the percentage of scores between 69 and 77, we need to calculate the z-scores for these values.

The z-score for 69 is calculated as (69 - 73) / 4 = -1. The z-score for 77 is calculated as (77 - 73) / 4 = 1. Using the empirical rule, we know that approximately 68% of the data falls within one standard deviation of the mean, so the percentage of scores between 69 and 77 is approximately 68%.

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