Final answer:
To find the interval that contains the 50th percentile for the length of the Appalachian Trail through each state, we need to determine the cumulative frequency of the data. Based on the given information, the interval that contains the 50th percentile is d. 500 to 600 miles.
Step-by-step explanation:
To find the interval that contains the 50th percentile for the length of the Appalachian Trail through each state, we need to determine the cumulative frequency of the data.
Based on the given information, we know that the x-axis of the histogram ranges from 32.5 to 100.5, and the width of each interval is 13.6. To find the cumulative frequency, we can calculate the cumulative sum of the frequencies in each interval.
The cumulative frequency for each interval is as follows:
Interval 1: From 32.5 to 46.1 miles - Cumulative Frequency: 5
Interval 2: From 46.1 to 59.7 miles - Cumulative Frequency: 10
Interval 3: From 59.7 to 73.3 miles - Cumulative Frequency: 20
Interval 4: From 73.3 to 86.9 miles - Cumulative Frequency: 35
Interval 5: From 86.9 to 100.5 miles - Cumulative Frequency: 50
Since the goal is to find the interval that contains the 50th percentile, we are looking for the interval where the cumulative frequency is closest to 50. In this case, that would be Interval 4, which ranges from 73.3 to 86.9 miles. Therefore, the correct answer is d. 500 to 600 miles.