To determine the intervals used for the frequency table, we can analyze the given data and constraints:
[tex]\[ \text{Data:}
\begin{pmatrix}
1207 & 1600 & 1800 & 2300 & 4200 \\
1380 & 1600 & 1850 & 2310 & 4260
\end{pmatrix}
\][/tex]
[tex]\[
\text{Frequency Table:}
\begin{tabular}{|c|c|c|}
\hline \multicolumn{3}{|c|}{ U.S. Bridges } \\
\hline Length (ft) & Tally & Frequency \\
\hline (first interval) & HHH II & 7 \\
\hline & & \\
\hline & & \\
\hline & & \\
\hline (last interval) & II & 2 \\
\hline
\end{tabular}
\][/tex]
Step-by-Step Solution:
1. Identify the Range of Data:
The minimum value in the data is 1207 feet, and the maximum value is 4260 feet.
2. Determine the Length of First Interval:
- The first interval tally "HHH II" translates to a frequency of 7.
- We need to assume what range could cover 7 values from the provided data.
3. Determine the Length of the Last Interval:
- The last interval tally is "II" with a frequency of 2.
- We need to assume what range would cover the remaining 2 values from the data.
4. Verify Potential Intervals:
Option (a): 4 intervals of 1000 feet:
- 4 intervals would cover a range of [tex]\( 4 \times 1000 = 4000 \)[/tex] feet.
- This option seems unlikely because 1207 to 4260 spans 3053 feet, which doesn’t fit 4 intervals neatly.
Option (b): 5 intervals of 1000 feet:
- 5 intervals would cover a range of [tex]\( 5 \times 1000 = 5000 \)[/tex] feet.
- This option also seems unlikely because the range 1207 to 4260 doesn't match 5000 feet length.
Option (c): 6 intervals of 500 feet:
- 6 intervals would cover a range of [tex]\( 6 \times 500 = 3000 \)[/tex] feet.
- This option seems initially reasonable.
Option (d): 7 intervals of 500 feet:
- 7 intervals would cover a range of [tex]\( 7 \times 500 = 3500 \)[/tex] feet.
- This should cover the data range from 1207 to 4260 if starting from a lower point.
5. Calculate Intervals for One Feasible Option:
Option (d): 7 intervals of 500 feet:
- The intervals would be: 1200-1700, 1700-2200, 2200-2700, 2700-3200, 3200-3700, 3700-4200, 4200-4700.
- Upon cross-verifying, we find that:
- For the first interval (1200-1700): 1207, 1600, 1380, 1600 - 4 values are already covered. We need 3 more for 7.
- For the last interval (4200-4700): 4200, 4260 - both values fit which are 2 values in range covered.
Thus, Jamie likely used 7 intervals of 500 feet each (Option d).
Answer: d. 7 intervals of 500 feet
