Question

a sample of college freshmen is surveyed and asked the following question: \what aspect of college were you least prepared for?\ all students in the sample answered this question, and the students were able to choose one of the following five options as their answer: academics, financial issues, social issues, life balance, and other. the percentages who chose each option are shown in the table below. if a college administrator decides to consider anyone who selected either social issues or life balance to fall within the category of \personal adjustment,\ and if it turns out that 1,260 students in the sample fall into this category of \personal adjustment,\ which of the following must have been the total sample size for this survey?

aspect of college	percentage
financial issues	14%
social issues	19%
life balance	17%
other	1%

3,600
3,500
3,450
3,400
its impossible to answer this question without more information.

Explanation:

Step1: Calculate percentage of "Personal Adjustment"

Add the percentages of Social Issues and Life Balance. $19\%+ 17\%=36\%$

Step2: Set up proportion to find total sample size

Let the total sample size be $x$. We know that $36\%$ of $x$ is $1260$. So the equation is $0.36x = 1260$.

Step3: Solve for $x$

Divide both sides of the equation by $0.36$. $x=\frac{1260}{0.36}=3500$

Answer:

3,500