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Answer :
Final answer:
About 34 percent of a normally distributed data set falls between a value one standard deviation below the mean and the mean itself; therefore, in this case, between 23 and 25.
Explanation:
The subject of this question is Mathematics, specifically dealing with the concept of a normal distribution within the topic of descriptive statistics. We are asked to determine which percentage of a normally distributed data set, with a mean of 25 and an unspecified standard deviation B, falls between the values 23 and 25. This question relates to the properties of the normal distribution and the empirical rule.
According to the empirical rule, for a normal distribution, approximately 68 percent of the data falls within one standard deviation of the mean. The range from 23 to 25 is a one standard deviation range on the left side of the mean since the mean is 25. Therefore, since half of this 68 percent falls below the mean and the other half above the mean, the percentage of data that falls between 23 and 25 represents approximately 34 percent of the data set. This information allows us to answer the student's question directly: the percentage of the data that falls between 23 and 25 is 34.0 percent (Option A).
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