Question

heights is bell - shaped and symmetric, with a center. a tree is considered “exceptionally tall” if its height places it among the tallest 10% of all trees of this species. based on this information, which one of the following statements is most accurate for a tree that is 1.1 feet above the center of the distribution? the tree is within 2% of the cutoff for the tallest 10%. because the distribution is symmetric, a tree this far above average has the same percentile as one equally far below average. there is not enough information available in this problem to answer the question. the tree lies exactly 1.1 standard deviations above the mean. the tree is well above the 90th percentile.

Explanation:

Step1: Analyze the 90th percentile

A tree is in the tallest 10% if it is above the 90th - percentile. We know the center of the distribution (mean). But we don't know the standard - deviation.

Step2: Evaluate each option

• Option 1: We don't know the standard - deviation, so we can't say it's within 2% of the cutoff for the tallest 10%.
• Option 2: Symmetry only tells us about the shape, not about the specific percentile without knowing the standard - deviation.
• Option 3: Correct. We need to know the standard - deviation of the distribution to determine percentiles and how many standard - deviations away a value is from the mean.
• Option 4: Without knowing the standard - deviation, we can't say it's exactly 1.1 standard - deviations above the mean.
• Option 5: Without knowing the standard - deviation, we can't say it's well above the 90th percentile.

Answer:

There is not enough information available in this problem to answer the question.