Students at a major university are complaining of a serious housingcrunch. Many of the university's students, they complain, have tocommute too far to school because there is not enough housing nearcampus. The university officials respond with the following information:the mean distance commuted to school by students is 15.4 miles, and thestandard deviation of the distance commuted is 3.6 miles.Assuming that the university officials' information is correct, completethe following statements about the distribution of commute distances forstudents at this university.(a) According to Chebyshev's theorem, at least 84% of the commutedistances lie between O miles and O miles. (Round your answer to 1 decimalplace.) standard deviation of the distance commuted is 3.6 miles.Assuming that the university officials' information is correct, completethe following statements about the distribution of commute distances forstudents at this university.(a) According to Chebyshev's theorem, at least 84% of the commutedistances lie between miles andplace.)miles. (Round your answer to 1 decimal(b) According to Chebyshev's theorem, at least (?of the commutedistances lie between 8.2 miles and 22.6 miles.

Answered: ce too far to scl . The universit

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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 15.4 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 84% of the commute
distances lie between O miles and O miles. (Round your answer to 1 decimal
place.)

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 84% of the commute
distances lie between miles and
place.)
miles. (Round your answer to 1 decimal
(b) According to Chebyshev's theorem, at least (?
of the commute
distances lie between 8.2 miles and 22.6 miles.

Expert Solution

Step 1

Chebyshev's Theorem is a fact that applies to all possible data sets. It describes the minimum proportion of the measurements that lie must within one, two, or more standard deviations of the mean.

Moreover, it says that at least 1- $\frac{1}{k^{2}}$ of the data lies between, mean $\pm k \times s \tan d a r d d e v i a t i o n .$

According to the given sum, we need to apply Chebyshev's theorem to find (a) and (b).

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