Question

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 16.2 miles, and the standard deviation of the distance commuted is 3.1 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 11.55 miles and 20.85 miles.

(b) According to Chebyshev's theorem, at least of the commute distances lie between 10.0 miles and 22.4 miles.

(c) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately of the commute distances lie between 10.0 miles and 22.4 miles.

(d) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 68% of the commute distances lie between miles and miles.

Answer 1

From the given information,

The correct answers are,

1. According to Chebyshev's theorem, at least 55.56% of the commute distances lie between 11.55 miles and 20.85 miles.

2. According to Chebyshev's theorem, at least of 75% the commute distances lie between 10.0 miles and 22.4 miles.

3.  Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 95% of the commute distances lie between 10.0 miles and 22.4 miles.

4. Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 68% of the commute distances lie between 13.1 miles and 19.3 miles.

Thank you.