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 16.2miles, and the standard deviation of the distance commuted is 4.0miles.

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

?56%75%84%89%

of the commute distances lie between 8.2 miles and 24.2 miles.

(b) According to Chebyshev's theorem, at least 36% of the commute distances lie between milesand miles. (Round your answer to 1 decimal place.)

(c) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 99.7% of the commute distances lie between milesand miles.

(d) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately

?68%75%95%99.7%

of the commute distances lie between 8.2 miles and 24.2 miles.