5. In 1994, if 20 percent of the first-year students who took the placement exam received a score of 85 or higher, approximately what percent of all first-year students received a score of 85 or higher on the placement exam that year?
Answer: C
Approximately 18 percent of all first-year students received a score of 85 or higher on the placement exam in 1994.
In 1994, it was reported that 20 percent of first-year students who took the placement exam scored 85 or higher. Given that this is a representative group, it can be inferred that approximately 18 percent of all first-year students achieved a similar score.
A) 30%
This option is incorrect as it overestimates the percentage of students who scored 85 or higher. The data indicates that only 20 percent of exam takers reached this score, making 30 percent an unrealistic figure based on the provided context.
B) 22%
While this option is a plausible estimate, it is still higher than the 20 percent figure provided for those who took the exam. The data does not support a higher percentage of all first-year students achieving scores over those who actually sat for the exam.
C) 18%
This option accurately reflects a reasonable estimate based on the information given. If 20 percent of the exam-taking population scored 85 or higher, and considering typical score distributions, it is logical to conclude that around 18 percent of the total first-year students would achieve this score.
D) 9%
This option is significantly lower than the data provided, indicating a misunderstanding of the score distribution. A figure of 9 percent does not align with the 20 percent of exam takers who scored 85 or higher.
E) 4.50%
This option is also incorrect as it suggests an even lower representation of students achieving a score of 85 or higher. It does not correlate with the 20 percent of those who took the exam, which indicates a lack of sufficient performance among the total first-year population.
Conclusion
The answer of 18 percent is the most accurate reflection of the data provided regarding first-year students' performance on the placement exam in 1994. All other options fail to accurately represent the situation outlined in the question, either by overestimating or underestimating the student performance based on the 20 percent statistic given.