Final answer:
Over 95% of the slash pine trees will have diameters between 7.6 and 18.6 inches, as this range covers more than two standard deviations below and three standard deviations above the mean in a normal distribution.
Step-by-step explanation:
To find the fraction of slash pine trees with diameters between 7.6 and 18.6 inches, assuming that the distribution of tree diameters is roughly mound-shaped, we will use the empirical rule for normal distributions. Given that the mean diameter is 12 inches with a standard deviation of 2.2 inches, we can calculate how many standard deviations away from the mean our range is.
The empirical rule states that about 68% of the data falls within one standard deviation of the mean, about 95% within two standard deviations, and about 99.7% within three standard deviations. In this case, 7.6 inches is approximately 2 standard deviations below the mean (12 - 2(2.2) = 7.6) and 18.6 inches is approximately 3 standard deviations above the mean (12 + 3(2.2) = 18.6). Therefore, we can deduce that between 7.6 and 18.6 inches, we are looking at the data within two standard deviations below the mean and three standard deviations above, which encompasses more than 95% but less than 99.7% of the tree diameters based on the empirical rule. Hence, the fraction of trees within this range is likely to be higher than 95%.