(a) According to Chebyshev\'s theorem, at least _________ of the fares lie betwe
ID: 3175435 • Letter: #
Question
(a) According to Chebyshev's theorem, at least _________ of the fares lie between 24.17 dollars and 35.45 .
(b) According to Chebyshev's theorem, at least _________ of the fares lie between 22.29 dollars and 37.33 .
(c) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately _________ of the fares lie between 22.29 dollars and 37.33 .
A major cab company in Chicago has computed its mean fare from O'Hare Airport to the Drake Hotel to be $, with a standard deviation of $. Based on this information, complete the following statements about the distribution of the company's fares from O'Hare Airport to the Drake Hotel. 29.81Explanation / Answer
According to Chebyshev's theorem, at least (1 - 1/k2) % of observations lie within k standard deviations from the mean.
a) Given,
Mean = 29.81, SD = 3.76
24.17 and 35.45 are 1.5 standard deviations below and above from the mean respectively. Hence,
At least (1 - 1/1.52) i.e. 5/9 of the fares lie between 24.17 and 35.45.
b) Given,
Mean = 29.81, SD = 3.76
22.29 and 37.33 are 2 standard deviations below and above from the mean respectively. Hence,
At least (1 - 1/22) i.e. 3/4 of the fares lie between 22.29 and 37.33.
c) 22.29 and 37.33 are 2 standard deviations below and above from the mean respectively. According to empirical rule, 95% of the observations lie between 2 standard deviations from the mean.
Hence,
According to the empirical rule, approximately 95% of the fares lie between 22.29 dollars and 37.33.
d) According to empirical rule, approximately 99.7% of the data lie between 3 standard deviations from the mean.
29.81 - 3(3.76) = 18.53
29.81 + 3(3.76) = 41.09
Hence,
Approximately 99.7% of the fares lie between 18.53 dollars and 41.09 dollars
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.