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Answer :
Final answer:
Approximately 68% of the values in the distribution are expected to fall between 25 and 37.
Explanation:
To find the percentage of values expected to fall between 25 and 37 in a distribution with a mean of 25 and a standard deviation of 6, we can use the empirical rule.
- First, we calculate the range within one standard deviation of the mean. Since the standard deviation is 6, one standard deviation below the mean is 25 - 6 = 19, and one standard deviation above the mean is 25 + 6 = 31.
- Next, we determine the percentage of values within this range. According to the empirical rule, approximately 68% of the values fall within one standard deviation of the mean.
- Finally, we calculate the percentage of values between 25 and 37 within this range. Since 25 is within one standard deviation of the mean, we can expect that a similar percentage of values will fall between 25 and 37. Therefore, approximately 68% of the values in the distribution are expected to fall between 25 and 37.
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