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The mean score of a competency test is 71 with a standard deviation of 5. Use the empirical rule to find the percentage of scores between 66 and 76.

User Cuban
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Final answer:

To find the percentage of scores between 66 and 76, we can use the empirical rule. Calculate the z-scores for 66 and 76, then find the area under the normal curve between these z-scores using a z-table. Finally, subtract the areas to the left and right of the z-scores from the total area to find the percentage.

Step-by-step explanation:

To use the empirical rule to find the percentage of scores between 66 and 76, we need to calculate the z-scores for these values. The formula for calculating the z-score is z = (x - mean) / standard deviation. For 66, the z-score would be (66 - 71) / 5 = -1. For 76, the z-score would be (76 - 71) / 5 = 1.

Next, we can use a z-table to find the area under the normal curve between these two z-scores. The area between -1 and 1 is approximately 0.6827. However, we want the percentage of scores between 66 and 76, so we subtract the area to the left of -1 (0.5 - 0.3413 = 0.1587) and the area to the right of 1 (0.5 - 0.3413 = 0.1587) from 0.6827.

The percentage of scores between 66 and 76 is approximately 0.6827 - 0.1587 - 0.1587 = 0.3653, or 36.53%.

User Derenio
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