An urban forestry department measured the trunk diameters, in inches, of a sample of oak trees in a municipal park. The table below summarizes the frequency distribution of the measurements.
| Trunk Diameter (inches) | Frequency |
|---|---|
| to | |
| to | |
| to | |
| to | |
| to |
Based on the table, what fraction of the trees with a trunk diameter of at least inches have a trunk diameter of less than inches?
- A
- Cevap
- C
- D
- E
Cevap
The fraction of trees with a trunk diameter of at least 15 inches that have a trunk diameter of less than 25 inches is 37/52.
To calculate the required fraction, first identify the subset of trees that have a trunk diameter of at least 15 inches. Summing the frequencies of the intervals 15–19, 20–24, 25–29, and 30–34 gives 15 + 22 + 11 + 4 = 52 trees. Next, identify how many of these 52 trees have a trunk diameter of less than 25 inches. These are the trees in the intervals 15–19 and 20–24, giving 15 + 22 = 37 trees. Therefore, the fraction of trees meeting the condition is 37/52.
Adım Adım Çözüm
Anahtar Kavram
Conditional relative frequencies and part-to-whole calculations from grouped data tables.
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