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

Question

BlackTom AI · Accepted Answer

To begin, I’ll restate the data and question in my own words to ensure understanding: we have a table of telephone calls by duration (in minutes) and the number of calls for each duration, and we’re asked for the proportion of calls that lasted 5 minutes or more.

Option a: 13.45%. This would imply a fraction around 0.1345. If we tried to map this to a fraction using the data, 13.45% is far smaller than the share of calls lasting 5 or more (which would be a substantial portion of the total). So this seems inconsistent with the table, since 5+ minutes includes two rows (5 minutes and 6 minutes) with counts 52 and 32, which total 84.

Option b: 35.29%. This percentage corresponds to the ratio 84 out of a total of 238 calls, since 84/238 ≈ 0.3529, or 35.29%. This aligns with adding the 5-minute (52 calls) and 6-minute (32 calls) entries to get 84, and summing all durations to get 238 as the total number of calls.

Option c: 84/236. This is attempted as a fraction form, but the denominator should reflect the actual total number of calls, which from the table sums to 238, not 236. Using 236 would yield a slightly different decimal value, which would not match the actual data.

Option d: 21.85%. This percentage would correspond to a fraction around 0.2185. If we compare it to the accurate 84/238 value, 84/238 ≈ 0.3529, so 21.85% is clearly not correct for the given data. It might correspond to an incorrect total or a miscalculation of the numerator or denominator.

Now, let’s verify the core computations explicitly: the number of calls lasting 5 minutes or more is the sum of the 5-minute and 6-minute rows: 52 + 32 = 84. The total number of calls is the sum across all minute categories: 12 + 34 + 48 + 60 + 52 + 32 = 238. Therefore, the exact proportion is 84/238.

Converting to a percentage: (84 ÷ 238) × 100 ≈ 35.29%. This confirms that the option matching the correct calculation is the one stating 35.29% (84/238).

In summary, option b represents the correct proportion when computed from the provided table data, since 84 of the 238 total calls lasted 5 minutes or longer, giving about 35.29%. The other choices are either mathematically inconsistent with the data (option c uses an incorrect denominator) or numerically inconsistent with the computed proportion (options a and d).

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

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