1. In a survey, a group of 50 randomly selected students at a college were asked if they use public transportation when traveling to the college. The table above shows the results of the survey. If there are 4600 students at the college, what is the most reasonable estimate for the number of students at the college who use public transportation when traveling to the college?Table: Use public transportation: 35, Do not use public transportation: 15*
Answer: E
The most reasonable estimate for the number of students at the college who use public transportation is 3220.
Based on the survey results, 35 out of 50 students use public transportation. This proportion can be used to estimate the total number of students at the college who likely use public transportation.
A) 2820
This option is incorrect because it underestimates the proportion of students using public transportation based on the survey results. Given the ratio of 35 out of 50, the estimate should be higher than this value.
B) 2920
This estimate is also too low when considering the survey results. The calculation based on the survey suggests a larger proportion of students using public transportation, thus making this option inaccurate.
C) 3020
Though this option is higher than the previous ones, it still does not accurately reflect the survey's findings. The estimate does not align closely with the calculated proportion of students using public transportation from the survey.
D) 3120
While this option is a more reasonable estimate, it still falls short of the correct calculation derived from the survey data. It does not fully account for the proportion of students using public transportation.
E) 3220
This option correctly reflects the proportion of students using public transportation based on the survey results. The calculation indicates that approximately 35% of the total student body uses public transportation, leading to the estimate of 3220 students.
Conclusion
The correct estimate of 3220 students aligns with the survey's findings, which indicate that 70% of the sampled students use public transportation. All other options fail to accurately represent this proportion, making them less valid estimates for the total student population.