Question - Analyzing Data in Two-Way Table for Fish Weight
Solution:
To solve this problem, we need to analyze the data in the two-way table provided. We’ll calculate the percentage for each statement and then determine which one is true.Statement A: All of the trout caught, 50% weighed less than 8 pounds.To evaluate this, we look only at the trout data:There were 12 trout caught that weighed less than 8 pounds, and 6 that weighed 8 pounds or more.Total trout caught = 12 + 6 = 18 trout.Percent weighing less than 8 pounds = (12 / 18) * 100% = 66.7% (not 50%).Statement B: All of the bass caught, 25% weighed 8 pounds or more.For the bass data:There were 4 bass caught that weighed 8 pounds or more, and 8 that weighed less.Total bass caught = 4 + 8 = 12 bass.Percent weighing 8 pounds or more = (4 / 12) * 100% = 33.3% (not 25%).Statement C: Of all the fish that weighed less than 8 pounds, 25% were trout.To evaluate this, consider only the fish that weighed less than 8 pounds:Trout that weighed less than 8 pounds = 12,Bass that weighed less than 8 pounds = 8,Total fish that weighed less than 8 pounds = 12 + 8 = 20 fish.Percent of these that were trout = (12 / 20) * 100% = 60% (not 25%).Statement D: Of all the fish caught, more than 50% were bass that weighed less than 8 pounds.We will compare the number of bass that weighed less than 8 pounds to the total number of fish.Bass less than 8 pounds = 8,Total fish caught = 18 (trout) + 12 (bass) = 30 fish.Percent of these that were bass weighing less than 8 pounds = (8 / 30) * 100% ≈ 26.7% (not more than 50%).From the calculations above, it's clear that none of the statements A, B, C, or D are true based on the information provided in the two-way table.
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