Question
In: Statistics and Probability
2) The file ‘Energy’ contains the per capita energy consumption (in kilowatt-hours), for each of the...
2) The file ‘Energy’ contains the per capita energy consumption (in kilowatt-hours), for each of the 50 states and the District of Columbia during a recent year.
a) Compute the mean, variance, and standard deviation for the population.
b) What proportion of these states has per capita energy consumption within + or – 1 standard deviation of the mean, within + or – 2 standard deviations of the mean, and within + or – 3 standard deviations of the mean?
c) Compare your findings with what would be expected based on the empirical rule.
d) Repeat a) through c) with the District of Columbia removed. Have the results changed?
| State | Kilowatt Hours |
| Wyoming | 24567 |
| D.C | 20073 |
| Kentucky | 19970 |
| South Carolina | 18865 |
| Alabama | 18399 |
| Louisiana | 17902 |
| Idaho | 17453 |
| Tennessee | 16993 |
| Washington | 16357 |
| Indiana | 16277 |
| Mississippi | 15885 |
| Arkansas | 15595 |
| Texas | 15059 |
| North Carolina | 15033 |
| West Virginia | 15022 |
| Ohio | 14593 |
| Nevada | 14511 |
| Georgia | 14465 |
| North Dakota | 14380 |
| Oregon | 14172 |
| Delaware | 13926 |
| Oklahoma | 13918 |
| Montana | 13743 |
| Nebraska | 13691 |
| Virginia | 13536 |
| Iowa | 13255 |
| Kansas | 12743 |
| Missouri | 12614 |
| Florida | 12393 |
| Wisconsin | 12103 |
| Arizona | 12067 |
| Minnesota | 12019 |
| Maryland | 11425 |
| Illinois | 10903 |
| South Dakota | 10806 |
| Michigan | 10491 |
| New Mexico | 10344 |
| Utah | 10273 |
| Colorado | 10002 |
| Maine | 9532 |
| Vermont | 9309 |
| Connecticut | 9081 |
| New Jersey | 8667 |
| Alaska | 8543 |
| New Hampshire | 8095 |
| Pennsylvania | 8006 |
| Hawaii | 7913 |
| Massachusetts | 7744 |
| New York | 7135 |
| Rhode Island | 6716 |
| California | 6396 |
Solutions
Expert Solution
a) Compute the mean, variance, and standard deviation for the population.
| Mean | 12999.22 |
| Variance | 14959701 |
| Standard Deviation | 3867.777 |
b) What proportion of these states has per capita energy consumption within + or – 1 standard deviation of the mean, within + or – 2 standard deviations of the mean, and within + or – 3 standard deviations of the mean?
| mean - 1s | 9,092.95 |
| mean + 1s | 16,905.48 |
| 64.7% | |
| mean - 2s | 5,186.69 |
| mean + 2s | 20,811.74 |
| 98.0% | |
| mean - 3s | 1,280.43 |
| mean + 3s | 24,718.01 |
| 100.0% |
c) Compare your findings with what would be expected based on the empirical rule.
The values according to the empirical rule will follow the rule 68-95-99.7% and the values are close to the empirical rule.
d) Repeat a) through c) with the District of Columbia removed. Have the results changed?
| Mean | 12857.74 |
| Variance | 14238111 |
| Standard Deviation | 3773.342 |
| mean - 1s | 9,046.09 |
| mean + 1s | 16,669.39 |
| 68.0% | |
| mean - 2s | 5,234.44 |
| mean + 2s | 20,481.04 |
| 98.0% | |
| mean - 3s | 1,422.79 |
| mean + 3s | 24,292.69 |
| 98.0% |
Yes, the results have changed.
orchestra answered 1 year agoRelated Solutions
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