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 officials respond with the following information: the mean distance commuted to school by students is 17.9 miles, and the standard deviation of the distance commuted is 3.6 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 ▼(Choose one) of the commute distances lie between 10.7 miles and 25.1miles. (b)According to Chebyshev's theorem, at least 84% of the commute distances lie between miles andmiles. (Round your answer to 1 decimal place.)

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...