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*
3220 students at the college use public transportation when traveling to the college.
The survey indicates that 35 out of 50 students use public transportation, which represents a proportion of 0.7 (or 70%). By applying this proportion to the total student population of 4600, we can estimate that approximately 3220 students utilize public transport.
To get 2820 as an estimate, one would assume a much lower proportion of students using public transportation than the survey suggests. This would imply a usage rate of only about 61.1% (2820/4600), which is not aligned with the 70% derived from the survey data.
An estimate of 2920 would imply that about 63.5% of the student population uses public transportation. This percentage is still significantly lower than the survey's findings of 70% and does not accurately reflect the data provided.
The estimate of 3020 corresponds to approximately 65.5% of the total student body. This figure further deviates from the 70% indicated in the survey results, leading to an underestimation of the actual number of students using public transport.
Choosing 3120 suggests a usage rate of around 67.8%. This is still below the surveyed proportion of 70%, resulting in a continued undercount of students who rely on public transportation.
To accurately estimate the number of students using public transportation at the college, the survey data showing that 70% of respondents use it must be applied to the total student population of 4600. This calculation clearly yields an estimate of 3220 students, which is the most reasonable and justified conclusion based on the information provided.
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