Statistics

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 Chebyshev's theorem, at least _____ of the commute distances lie between 9.9 miles and 25.5 miles.

(b) According to Chebyshev's theorem, at least _____ of the commute distances lie between 7.95 miles and 27.45 miles.

(c) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately_____  of the commute distances lie between 9.9 miles and 25.5 miles.

(d) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 99.7% of the commute distances lie between ___miles and ____