Final answer:
The question involves the normal distribution of slash pine tree diameters. The range given falls within two standard deviations of the mean, so approximately 95% of the trees will have diameters within that range.
Step-by-step explanation:
The question is asking what fraction of the slash pine trees will have diameters between 10.4 and 24.4 inches given that the mean diameter is 16 inches with a standard deviation of 2.8 inches. This is a statistics problem involving the properties of the normal distribution. For a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.
Given that the range from 10.4 to 24.4 inches spans from 2 standard deviations below the mean to 2 standard deviations above the mean (16 - 2(2.8) = 10.4 and 16 + 2(2.8) = 24.4), we can use the empirical rule to determine the fraction of trees in this range.
Therefore, the correct answer is (b) Approximately 95%, since the range of diameters spans 4 standard deviations, covering approximately 95% of the distribution around the mean.