What proportion of telephone calls lasted 5 minutes or more?

Question

BlackTom AI · Accepted Answer

First, I restate the data to ensure we’re using the right numbers: the table shows minutes and number of calls for each duration from 1 to 6 minutes, and the provided list includes four answer choices.

Option a. 21.85%: To evaluate this, we’d look for a ratio around 0.2185. If we sum the counts for 1, 2, 3, and 4 minutes (12 + 34 + 48 + 60) we get 154 calls, but that would correspond to the proportion of calls lasting up to 4 minutes, not 5 minutes or more. The 21.85% figure would come from 52 out of 238 (which is 21.85%), i.e., only the 5-minute bucket, not 5 minutes or more. So this option misinterprets the threshold by excluding the 6-minute calls.

Option b. 84/236: This option presents a fraction form. We would need a total of 236 in the denominator, which does not match the counts in the table (the total is 238). The numerator 84 could correspond to calls lasting 5 or more minutes (52 + 32 = 84), but the denominator is incorrect here, making this option invalid.

Option c. 35.29%: This matches the calculation for 5 minutes or more. The total number of calls is 238 (sum of all years: 12 + 34 + 48 + 60 + 52 + 32). The number of calls lasting 5 minutes or more is 52 (at 5 minutes) plus 32 (at 6 minutes) = 84. Therefore, 84/238 = 0.3529, which is 35.29%. This option aligns with the correct pool and the correct numerator.

Option d. 13.45%: This would correspond to a very small subset, like 32 out of 238 is about 13.45%, which would be just the 6-minute bucket. But since the question asks for 5 minutes or more, we must include both 5- and 6-minute calls, not just the 6-minute bucket alone. Thus this percentage is incorrect.

Putting it together, the only choice that correctly reflects the proportion of calls lasting 5 minutes or more (i.e., 84 calls out of 238 total) is the 35.29% result, since 84 ÷ 238 = 0.3529 ≈ 35.29%.

What proportion of telephone calls lasted 5 minutes or more?

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