Answers:
B) 66%C) 34%See the diagram belowC) 86% of the people who studied passed the quiz.
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Explanations:
Problem 1
We have B = 62+32 = 94 people who wear a belt. Of this total, A = 62 belt wearers also have a watch. So A/B = 62/94 = 0.6596 = 65.96% = 66% of the belt wearers have a watch. This value is approximate.
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Problem 2
In the previous problem we found that roughly 66% of the belt wearers have a watch. This must mean about 100% - 66% = 34% of the belt wearers do not have a watch.
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Problem 3
The question is "Among left handers, what proportion has neat handwriting?" which means we're effectively only concerned with the first row that says "left-handed". In this row, there are 5 who write neat, and 10 who do not. We have B = 5+10 = 15 people who are left-handed. We'll divide everything in this row by this value of B.
So for A = 5, it turns into the approximate proportion A/B = 5/15 = 0.33 meaning that about 33% of the left-handers have neat handwriting.
For the other value in this row, A = 10 turns into A/B = 10/15 = 0.67 = meaning that about 67% of the left-handers have messy hand writing.
You'll do the same thing for row 2, but you'll divide everything by B = 65 (because there are 34+31 = 65 right-handed people total).
The filled out table is shown below.
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Problem 4
Let's say we ignore the percentage signs. Adding the values across the first row gets us B = 86+14 = 100 people who passed the quiz. Of that, A = 86 people who passed also studied as shown in the top left corner.
We can then see that A/B = 86/100 = 86% of the people who passed the quiz also studied. Notice the phrasing here. It's not the other way around. We would not say "86% of the people who studied passed the quiz". Your teacher has the order swapped unfortunately. If choice C said "86% of the people who passed the quiz studied for the test", then it would be fully correct. However, I think that's what they were going for and made a typo.
If we did state that "86% of the people who studied passed the quiz", then we'd be considering the first column instead of the first row. However, note how the percentages in the first column do not add to 100%.
