Answer :
Final answer:
The 68-95-99.7 rule is a statistical rule that applies to normal distributions. It states that approximately 68% of the data falls within one standard deviation of the mean, about 95% falls within two standard deviations, and roughly 99.7% falls within three standard deviations. To find the percentage of trees with diameters below 2.6 inches, we need to determine the number of standard deviations below the mean 2.6 inches is and use the 68-95-99.7 rule to approximate the percentage.
Explanation:
The 68-95-99.7 rule, also known as the empirical rule or the three-sigma rule, is a statistical rule that applies to normal distributions. It states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, about 95% falls within two standard deviations, and roughly 99.7% falls within three standard deviations.
In this case, the question asks about the percentage of trees with diameters below 2.6 inches. To find this, we need to determine the number of standard deviations below the mean 2.6 inches is. Once we know that, we can use the 68-95-99.7 rule to approximate the percentage of trees with diameters below 2.6 inches.
To find the number of standard deviations below the mean, we need to know the mean and standard deviation of the tree diameters. Once we have that information, we can calculate the z-score for 2.6 inches and use it to find the approximate percentage of trees below that diameter.
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