# Chebyshev’s theorem and the empirical rule Students at a major university are complaining of a serious housing crunch. Many of the university’s students, they complain, have to commute too far to school because there is not enough housing near campus. The university officials respond with the following information: the mean distance commuted to school by students is miles, and the standard deviation of the distance commuted is 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 Chebys hev’s theorem , at leas t ? of the com m ute dis tances lie between 10.0 m iles and 24.0 m iles . (b) According to Chebys hev’s theorem , at leas t ? of the com m ute dis tances lie between 8.25 m iles and 25.75 m iles . (c) Suppos e that the dis tribution is bell-s haped. According to the em pirical rule, approxim ately ? of the com m ute dis tances lie between 10.0 m iles and 24.0 m iles . (d) Suppos e that the dis tribution is bell-s haped. According to the em pirical rule, approxim ately 99.7% of the com m ute dis tances lie between miles and miles.

Chebyshev’s theorem and the empirical rule
Students at a major university are complaining of a serious housing crunch. Many of the university’s students, they complain, have to commute too far to school because there is not enough housing near campus. The university officials respond with the following information: the mean distance commuted to school by students is miles, and the standard deviation of the distance commuted is 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 Chebys hev’s theorem , at leas t ? of the com m ute dis tances lie between 10.0 m iles and 24.0 m iles .

(b) According to Chebys hev’s theorem , at leas t ? of the com m ute dis tances lie between 8.25 m iles and 25.75 m iles .

(c) Suppos e that the dis tribution is bell-s haped. According to the em pirical rule, approxim ately ? of the com m ute dis tances lie between 10.0 m iles and 24.0 m iles .

(d) Suppos e that the dis tribution is bell-s haped. According to the em pirical rule, approxim ately 99.7% of the com m ute dis tances lie between miles and miles.