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 17.5 miles, and the standard deviation of the distance commuted is 3.3 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 10.9 miles and 24.1 miles. (b) According to Chebyshev's theorem, at least 36% of the commute distances lie between miles and miles. (Round your answer to 1 decimal place.)
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Assuming that the university officials' information is correct, complete the following statements about the distribution of commute distances for students at this university.
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(a) According to Chebyshev's theorem, at least of the commute distances lie between
10.9
24.1
(b) According to Chebyshev's theorem, at least
36%
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