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 2 years ago
Next > < Previous

Related Solutions

The per capita energy consumption level​ (in kilowatt-hours) in a certain country for a recent year...
The per capita energy consumption level​ (in kilowatt-hours) in a certain country for a recent year can be approximated by a normal​ distribution, as shown in the figure. Mean=2296 Standard deviation=581.8 ​(a) What consumption level represents the 5 th ​percentile? ​ (b) What consumption level represents the 17 th ​percentile? ​(c) What consumption level represents the third ​quartile?
The per capita energy consumption level​ (in kilowatt-hours) in a certain country for a recent year...
The per capita energy consumption level​ (in kilowatt-hours) in a certain country for a recent year can be approximated by a normal​ distribution, as shown in the figure. ​(a) What consumption level represents the 7th ​percentile? ​(b) What consumption level represents the 21st ​percentile? ​(c) What consumption level represents the third ​quartile? mean=2302 SD=584.5
According to the International Atomic Energy Agency, per capita electricity consumption in Canada was 16,939 kWh...
According to the International Atomic Energy Agency, per capita electricity consumption in Canada was 16,939 kWh in 2002. A random sample of 51 households was monitored for one year to determine electricity usage. If the population standard deviation of annual usage is 3,500 kWh, what is the probability that the sample mean will be each of the following? a.More than 18,000 kWh b.More than 17,500 kWh c.Between 17,000 kWh and 18,000 kWh d.Less than 16,000 kWh e.Less than 15,000 kWh
The annual per capita consumption of bottled water was 32.6 gallons. Assume that the per capita...
The annual per capita consumption of bottled water was 32.6 gallons. Assume that the per capita consumption of bottled water is approximately normally distributed with a mean of 32.6 and a standard deviation of 10 gallons. a. What is the probability that someone consumed more than 43 gallons of bottled water? b. What is the probability that someone consumed between 30 and 40 gallons of bottled water? c. What is the probability that someone consumed less than 30 gallons of bottled water? d. 90%...
The annual per capita consumption of bottled water was 32.8 gallons. Assume that the per capita...
The annual per capita consumption of bottled water was 32.8 gallons. Assume that the per capita consumption of bottled water is approximately normally distributed with a mean of 32.8 and a standard deviation of 10 gallons. a. What is the probability that someone consumed more than 43 gallons of bottled​ water? b. What is the probability that someone consumed between 30 and 40 gallons of bottled​ water? c. What is the probability that someone consumed less than 30 gallons of...
The annual per capita consumption of bottled water was 30.5 gallons. Assume that the per capita...
The annual per capita consumption of bottled water was 30.5 gallons. Assume that the per capita consumption of bottled water is approximately normally distributed with a mean of 30.5 and a standard deviation of 10 gallons. a. What is the probability that someone consumed more than 31 gallons of bottled​ water? b. What is the probability that someone consumed between 20 and 30 gallons of bottled​ water? c. What is the probability that someone consumed less than 20 gallons of...
The annual per capita consumption of bottled water was 31.2 gallons. Assume that the per capita...
The annual per capita consumption of bottled water was 31.2 gallons. Assume that the per capita consumption of bottled water is approximately normally distributed with a mean of 31.2 and a standard deviation of 12 gallons. a. What is the probability that someone consumed more than 36 gallons of bottled​ water? b. What is the probability that someone consumed between 25 and 35 gallons of bottled​ water? c. What is the probability that someone consumed less than 25 gallons of...
The annual per capita consumption of bottled water was 34.334.3 gallons. Assume that the per capita...
The annual per capita consumption of bottled water was 34.334.3 gallons. Assume that the per capita consumption of bottled water is approximately normally distributed with a mean of 34.334.3 and a standard deviation of 1212 gallons. a. What is the probability that someone consumed more than 4444 gallons of bottled​ water? b. What is the probability that someone consumed between 3030 and 4040 gallons of bottled​ water? c. What is the probability that someone consumed less than 3030 gallons of...
The annual per capita consumption of bottled water was 32.7 gallons. Assume that the per capita...
The annual per capita consumption of bottled water was 32.7 gallons. Assume that the per capita consumption of bottled water is approximately normally distributed with a mean of 32.7 and a standard deviation of 10 gallons. a. What is the probability that someone consumed more than 33 gallons of bottled​ water? b. What is the probability that someone consumed between 20 and 30 gallons of bottled​ water? c. What is the probability that someone consumed less than 20 gallons of...
The annual per capita consumption of bottled water was 32.8 gallons. Assume that the per capita...
The annual per capita consumption of bottled water was 32.8 gallons. Assume that the per capita consumption of bottled water is approximately normally distributed with a mean of 32.8 and a standard deviation of 11 gallons. A. What is the probability that someone consumed more than 43 gallons of bottled​water? B. What is the probability that someone consumed between 20 and 30 gallons of bottled​ water? C. What is the probability that someone consumed less than 20 gallons of bottled​water?...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT