Students at a major university are complaining of a serious housing crunch. They complain that many students have to commute too far to school because there is not enough housing near campus. University officlals respond with the following information: the mean distance commuted to school by students is 17.2 miles, and the standard deviation of the distance commuted is 3.7 miles. Assuming that the university officials' information is correct, complete the following statements about the distribution of commute distances for students at this university. (a) According to Chebyshev's theorem, at least $84 \%$ of the commute distances lie between $\square$ miles and $\square$ miles. (Round your answer to 1 decimal place.) (b) According to Chebyshev's theorem, at least (Choose one) $\nabla$ of the commute distances lie between 9.8 miles and 24.6 miles.

Step 1 ：Given that the mean distance commuted to school by students is 17.2 miles and the standard deviation of the distance commuted is 3.7 miles.

Step 2 ：According to Chebyshev's theorem, at least \(1 - \frac{1}{k^2}\) of the data lies within k standard deviations of the mean, where k is any positive integer.

Step 3 ：For part (a), we need to find a k such that \(1 - \frac{1}{k^2}\) is at least 0.84. Solving this equation gives k approximately equal to 2.5.

Step 4 ：We can calculate the range by subtracting and adding k standard deviations from the mean. This gives us a lower bound of \(17.2 - 2.5 \times 3.7 = 7.95\) miles and an upper bound of \(17.2 + 2.5 \times 3.7 = 26.45\) miles.

Step 5 ：Final Answer: (a) According to Chebyshev's theorem, at least \(84 \%\) of the commute distances lie between \(\boxed{7.9}\) miles and \(\boxed{26.5}\) miles.

Step 6 ：For part (b), we need to find the percentage of commute distances that lie between 9.8 miles and 24.6 miles. This range is equivalent to the mean minus 2 standard deviations and the mean plus 2 standard deviations.

Step 7 ：According to Chebyshev's theorem, at least \(1 - \frac{1}{k^2}\) of the data lies within k standard deviations of the mean. In this case, k is 2, so at least \(1 - \frac{1}{2^2} = 0.75\) or 75% of the data lies within this range.

Step 8 ：Final Answer: (b) According to Chebyshev's theorem, at least \(\boxed{75 \%}\) of the commute distances lie between 9.8 miles and 24.6 miles.