Final answer:
(e) 7 feet The standard deviation of 7 feet indicates the spread or variability of tree heights around the mean of 28.7 feet in the park. It signifies that most tree heights lie within approximately 7 feet above or below the mean.
Explanation:
The standard deviation of the heights of trees in the park is 7 feet. This can be deduced by using the Z-score formula, where the Z-score corresponding to the 0.4% percentile (which is -2.65 approximately) is calculated by finding the inverse of the cumulative distribution function of a standard normal distribution. Using the formula Z = (X - μ) / σ, where X is the value (18.1 feet), μ is the mean (28.7 feet), and Z is the Z-score, the standard deviation (σ) can be calculated. Rearranging the formula to solve for σ yields σ = (X - μ) / Z. Plugging in the values, σ = (18.1 - 28.7) / (-2.65) ≈ 7 feet.
The standard deviation of 7 feet indicates the spread or variability of tree heights around the mean of 28.7 feet in the park. It signifies that most tree heights lie within approximately 7 feet above or below the mean. The lower Z-score for the 0.4% percentile suggests that the height of 18.1 feet is significantly below the mean, indicating it is quite rare within this distribution. This statistical measurement helps understand the distribution pattern and the likelihood of tree heights falling within certain ranges in the park.