What proportion of telephone calls lasted 5 minutes or more?[Fill in the blank]

Question

BlackTom AI · Accepted Answer

Proportion equals the number of favorable cases divided by the total number of cases, so start by identifying calls of length 5 minutes or more and the total number of calls.

1. Relevant knowledge points and concepts
- Proportion = (count of interest) / (total count).
- Percent = proportion × 100.
- When reporting a percent, round as requested (here to two decimal places).

2. Step-by-step reasoning
- From the table, calls lasting 5 minutes = 52 and calls lasting 6 minutes = 32.
- Count of calls lasting 5 minutes or more = 52 + 32 = 84.
- Total number of calls = sum of all frequencies: 12 + 34 + 48 + 60 + 52 + 32.

3. Intermediate calculations
- Total: 12 + 34 = 46; 46 + 48 = 94; 94 + 60 = 154; 154 + 52 = 206; 206 + 32 = 238.
- Proportion = 84 / 238.
- Decimal: 84 ÷ 238 = 0.352941176...
- Percent: 0.352941176 × 100 = 35.2941176%.
- Rounded to two decimal places = 35.29%.

4. Why this answer is correct
The numerator correctly counts all calls lasting at least 5 minutes (both 5- and 6-minute calls). The denominator is the correct total number of calls (all minutes 1–6). Converting the fraction to a percent and rounding yields 35.29%, matching the provided answer.

5. Why the other options are incorrect
- a. 84/236 uses an incorrect total (236 instead of 238), so its decimal would differ.
- c. 21.85% equals 52/238 (only the 5-minute calls), so it omits the 6-minute calls.
- d. 13.45% equals 32/238 (only the 6-minute calls), so it omits the 5-minute calls.

Conclusion: The correct proportion of telephone calls lasting 5 minutes or more is 35.29%, which matches the provided answer.

What proportion of telephone calls lasted 5 minutes or more?[Fill in the blank]Single choice

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