Question

health a university surveyed students at the university about their exercise habits. of those surveyed, 23.4% reported exercising for 20 minutes or longer at least four times per week. the survey had a margin of error of ±2.9%. round to the nearest tenth, if necessary. the range of the actual percentages of students at the university who would report exercising for 20 minutes or longer at least four times per week is % to %. of the estimated 20,782 students at the university, it is expected that between and would report exercising for 20 minutes or longer at least four times per week.

Explanation:

Step1: Calculate the lower - bound percentage

Subtract the margin of error from the surveyed percentage. The surveyed percentage is $23.4\%$ and the margin of error is $2.9\%$. So the lower - bound percentage is $23.4 - 2.9=20.5\%$.

Step2: Calculate the upper - bound percentage

Add the margin of error to the surveyed percentage. So the upper - bound percentage is $23.4 + 2.9 = 26.3\%$.

Step3: Calculate the lower - bound number of students

Multiply the lower - bound percentage (in decimal form) by the total number of students. The total number of students is $20782$. The lower - bound percentage in decimal form is $0.205$. So the lower - bound number of students is $0.205\times20782=20782\times0.205 = 4260.31\approx4260$.

Step4: Calculate the upper - bound number of students

Multiply the upper - bound percentage (in decimal form) by the total number of students. The upper - bound percentage in decimal form is $0.263$. So the upper - bound number of students is $0.263\times20782=20782\times0.263 = 5465.666\approx5466$.

Answer:

The range of the actual percentages of students at the university who would report exercising for 20 minutes or longer at least four times per week is $20.5\%$ to $26.3\%$.
Of the estimated 20782 students at the university, it is expected that between $4260$ and $5466$ would report exercising for 20 minutes or longer at least four times per week.