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

Question

BlackTom AI · Accepted Answer

Proportion = (number of calls lasting ≥ 5 minutes) ÷ (total number of calls).

Relevant concepts: a proportion is a fraction of the whole; to convert to a percent multiply by 100. Here “5 minutes or more” includes calls of length 5 and 6 minutes.

Step-by-step reasoning and calculations:
1. Read frequencies from the table:
   - 1 minute: 12 calls
   - 2 minutes: 34 calls
   - 3 minutes: 48 calls
   - 4 minutes: 60 calls
   - 5 minutes: 52 calls
   - 6 minutes: 32 calls
2. Compute total number of calls:
   - Total = 12 + 34 + 48 + 60 + 52 + 32
   - Total = 46 + 48 + 60 + 52 + 32 = 94 + 60 + 52 + 32 = 154 + 52 + 32 = 206 + 32 = 238
3. Compute number of calls lasting 5 minutes or more:
   - Calls ≥5 min = calls of 5 min + calls of 6 min = 52 + 32 = 84
4. Form the proportion and convert to percent:
   - Proportion = 84 / 238
   - Decimal = 84 ÷ 238 ≈ 0.3529411765
   - Percent ≈ 0.3529411765 × 100% = 35.29411765% ≈ 35.29%

Why the correct answer is correct:
- The numerator (84) counts all calls of length 5 and 6 minutes, and the denominator (238) is the correct total of all calls, giving 84/238 ≈ 35.29%.

Why the other options are incorrect:
- (a) 21.85% equals 52/238, which counts only 5‑minute calls (not “5 or more”).
- (c) 13.45% equals 32/238, which counts only 6‑minute calls.
- (d) 84/236 uses the correct numerator but an incorrect total (236 instead of 238), so its value is slightly off.

Conclusion: The proportion of calls lasting 5 minutes or more is 35.29%, matching answer b.

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