compare chebyshevs rule and the empirical rule.\na. compare the estimates given by the two rules for the…

compare chebyshevs rule and the empirical rule.\na. compare the estimates given by the two rules for the percentage of observations that lie within two standard deviations to either side of the mean. comment on the differences.\nb. compare the estimates given by the two rules for the percentage of observations that lie within three standard deviations to either side of the mean. comment on the differences.\nusing the empirical rule, find the estimate for the percentage of observations that lie within two standard deviations to either side of the mean.\napproximately 95% of the observations in any data set lie within 2 standard deviations to either side of the mean.\n(type an integer or a decimal. do not round.)\nselect the best answer that describes the differences in the two rules.\na. chebyshevs rule is for a data set that is roughly bell shaped and gives the percentage of the least number of observations that are definitely included in the area. the empirical rule is for any quantitative data set and gives the percentage that approximates the number of observations that could be included in the area. in this case, chebyshevs rule captures more of the observations in the area.\nb. chebyshevs rule is for any quantitative data set and gives the percentage that approximates the number of observations that could be included in the area. the empirical rule is for a data set that is roughly bell shaped and gives the percentage of the least number of observations that are definitely included in the area. in this case, the empirical rule captures more of the observations in the area.\nc. chebyshevs rule is for any quantitative data set and gives the percentage of the least number of observations that are definitely included in the area. the empirical rule is for a data set that is roughly bell shaped and gives the percentage that approximates the number of observations that could be included in the area. in this case, the empirical rule captures more of the observations in the area.\napproximately\nfor a data set that is roughly bell shaped and gives the percentage\nthe number of observations that could be included in the area. the\nany quantitative data set and gives the percentage of the least\nat most\nof the observations in the area.\nexactly\ngiven by the two rules for the percentage of observations that lie\nitions to either side of the mean. comment on the differences.\nat least\nd the estimate for the percentage of observations that lie within three\ner side of the mean.\n% of the observations in any data set lie within 3 standard deviations to either side of the mean.\n(round to the nearest integer as needed.)

compare chebyshevs rule and the empirical rule.\na. compare the estimates given by the two rules for the percentage of observations that lie within two standard deviations to either side of the mean. comment on the differences.\nb. compare the estimates given by the two rules for the percentage of observations that lie within three standard deviations to either side of the mean. comment on the differences.\nusing the empirical rule, find the estimate for the percentage of observations that lie within two standard deviations to either side of the mean.\napproximately 95% of the observations in any data set lie within 2 standard deviations to either side of the mean.\n(type an integer or a decimal. do not round.)\nselect the best answer that describes the differences in the two rules.\na. chebyshevs rule is for a data set that is roughly bell shaped and gives the percentage of the least number of observations that are definitely included in the area. the empirical rule is for any quantitative data set and gives the percentage that approximates the number of observations that could be included in the area. in this case, chebyshevs rule captures more of the observations in the area.\nb. chebyshevs rule is for any quantitative data set and gives the percentage that approximates the number of observations that could be included in the area. the empirical rule is for a data set that is roughly bell shaped and gives the percentage of the least number of observations that are definitely included in the area. in this case, the empirical rule captures more of the observations in the area.\nc. chebyshevs rule is for any quantitative data set and gives the percentage of the least number of observations that are definitely included in the area. the empirical rule is for a data set that is roughly bell shaped and gives the percentage that approximates the number of observations that could be included in the area. in this case, the empirical rule captures more of the observations in the area.\napproximately\nfor a data set that is roughly bell shaped and gives the percentage\nthe number of observations that could be included in the area. the\nany quantitative data set and gives the percentage of the least\nat most\nof the observations in the area.\nexactly\ngiven by the two rules for the percentage of observations that lie\nitions to either side of the mean. comment on the differences.\nat least\nd the estimate for the percentage of observations that lie within three\ner side of the mean.\n% of the observations in any data set lie within 3 standard deviations to either side of the mean.\n(round to the nearest integer as needed.)

Answer

Brief Explanations:

Chebyshev's rule applies to any quantitative data - set and gives the percentage of the least number of observations that are definitely included in the area within a certain number of standard - deviations from the mean. The empirical rule applies to roughly bell - shaped data sets and gives an approximation of the percentage of observations in the area within a certain number of standard - deviations from the mean. For two standard - deviations from the mean, the empirical rule says approximately 95% of observations in a bell - shaped data set lie within this range. For three standard - deviations from the mean, the empirical rule says approximately 99.7% of observations in a bell - shaped data set lie within this range. Chebyshev's rule for (k = 2) gives (1-\frac{1}{k^{2}}=1 - \frac{1}{4}=75%) (at least) and for (k = 3) gives (1-\frac{1}{k^{2}}=1-\frac{1}{9}\approx89%) (at least).

Answer:

a. Using Chebyshev's rule, at least (75%) of the observations lie within two standard deviations of the mean. Using the empirical rule, approximately (95%) of the observations lie within two standard deviations of the mean in a roughly bell - shaped data set. The empirical rule gives a higher percentage for bell - shaped data sets compared to Chebyshev's rule which is a more general result for any quantitative data set. b. Using Chebyshev's rule, at least (89%) of the observations lie within three standard deviations of the mean. Using the empirical rule, approximately (99.7%) of the observations lie within three standard deviations of the mean in a roughly bell - shaped data set. The empirical rule gives a higher percentage for bell - shaped data sets compared to Chebyshev's rule. c. C. Chebyshev's rule is for any quantitative data set and gives the percentage of the least number of observations that are definitely included in the area. The empirical rule is for a data set that is roughly bell - shaped and gives the percentage that approximates the number of observations that could be included in the area. d. Approximately (99.7%) (using the empirical rule for bell - shaped data sets) and at least (89%) (using Chebyshev's rule for any quantitative data set) of the observations lie within three standard deviations of the mean.