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Answer :
Final answer:
About 34.0% of the data from a normally distributed data set with a mean of 25 and a standard deviation of 2 falls between 23 and 25.
Explanation:
When considering a normally distributed data set with a given mean and standard deviation, we can apply the Empirical Rule to determine the percentage of data that falls within a certain range. For a data set with a mean of 25 and a standard deviation of 2, approximately 68 percent of the data falls within one standard deviation of the mean. This means that 68 percent of the data falls between 23 (25 - 2) and 27 (25 + 2).
Since the question asks for the percentage of the data that falls between 23 and 25, we are looking at half of the data within one standard deviation above the mean. The Empirical Rule states that about 34% of the data falls between the mean and one standard deviation above it, and another 34% falls between the mean and one standard deviation below it. Therefore, the answer to the question is A) 34.0%.
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Answer:
Step-by-step explanation:
To find the percentage of the data falling between 23 and 25 in a normally distributed data set with a mean of 25 and a standard deviation of 2, we can use the empirical rule for normally distributed data:
Approximately 68% of the data falls within one standard deviation of the mean.
Approximately 95% of the data falls within two standard deviations of the mean.
Approximately 99.7% of the data falls within three standard deviations of the mean.
Since the interval of interest is from 23 to 25, which is within one standard deviation below and above the mean, approximately 68% of the data falls within this interval.
So, the correct answer is:
B) 68.0
