Question

a teacher collected data from students to track whether they had completed the test review before their most recent test and whether they passed the test. the table below shows the relative frequencies.

	passed test	did not pass test	total
did not complete test review	13%	21%	34%
total	71%	29%	100%

what percentage of students who completed the test review passed the test?
options: 58%, 71%, 81.85%, 87.88%

Explanation:

Step1: Identify relevant data

From the table, the percentage of students who completed the test review and passed the test is 58%, and the percentage of students who completed the test review (total) is 66%.

Step2: Calculate the percentage

To find the percentage of students who completed the test review and passed, we use the formula: $\text{Percentage} = \frac{\text{Completed and Passed}}{\text{Total Completed}} \times 100\%$. Substituting the values, we get $\frac{58\%}{66\%} \times 100\% \approx 87.88\%$. Wait, no, wait. Wait, actually, the table's "Completed Test Review" row for "Passed Test" is 58% and "Total" for "Completed Test Review" is 66%? Wait, no, looking at the table again:

Wait the table columns: Passed Test, Did Not Pass Test, Total. Rows: Completed Test Review, Did Not Complete Test Review, Total.

So for "Completed Test Review" row: Passed Test is 58%, Did Not Pass Test is 8%, Total is 66% (58+8=66).

We need the percentage of students who completed the test review (so within the "Completed Test Review" group) who passed the test. So that's (Passed and Completed) / (Total Completed) 100% = 58% / 66% 100% ≈ 87.88%, which is approximately 87.88%, close to 87.88% (option D? Wait the options are 58%, 71%, 81.88%, 87.88%? Wait the image shows options: 58%, 71%, 81.88%, 87.88%? Wait the user's image: the options are 58%, 71%, 81.88%, 87.88%? Wait the calculation: 58 (completed and passed) divided by 66 (total completed) is 58/66 ≈ 0.8788, so 87.88%.

Wait, maybe I misread. Let's check again. The table:

• Completed Test Review: Passed Test 58%, Did Not Pass 8%, Total 66% (58+8=66)
• Did Not Complete Test Review: Passed 13%, Did Not Pass 21%, Total 34% (13+21=34)
• Total: Passed 71% (58+13), Did Not Pass 29% (8+21), Total 100% (66+34)

So the question is: What percentage of students who completed the test review passed the test? So it's (number of students who completed and passed) / (number of students who completed) 100%. Using the relative frequencies (since they are percentages of total), so 58% (completed and passed) divided by 66% (total completed) 100% = (58/66)*100 ≈ 87.88%.

Step3: Match with options

The option closest to 87.88% is 87.88% (the last option).

Answer:

87.88% (the option corresponding to 87.88%, likely the last one in the options shown: 87.88%)