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Chapter 3: Problem 30

Data on residential energy consumption per capita (measured in million BTU) had a mean of \(70.8\) and a standard deviation of \(7.3\) for the states east of the Mississippi River. Assume that the distribution of residential energy use if approximately unimodal and symmetric. a. Between which two values would you expect to find about \(68 \%\) of the per capita energy consumption rates? b. Between which two values would you expect to find about \(95 \%\) of the per capita energy consumption rates? c. If an eastern state had a per capita residential energy consumption rate of 54 million BTU, would you consider this unusual? Explain. d. Indiana had a per capita residential energy consumption rate of \(80.5\) million BTU. Would you consider this unusually high? Explain.

Short Answer

Expert verified
a. The 68% of the per capita energy consumption rates would lie between 63.5 and 78.1 million BTU. b. The 95% of the per capita energy consumption rates would lie between 56.2 and 85.4 million BTU. c. The per capita residential energy consumption rate of 54 million BTU for an eastern state is indeed unusual, as it falls beyond 2 standard deviations from the mean. d. Indiana's per capita residential energy consumption rate of 80.5 million BTU is high, but not unusually high as it lies within 2 standard deviations range.

Step by step solution

01

Calculating values for 68% data

Under normal distribution, about 68% of the data falls within 1 standard deviation of the mean. Calculate the upper and lower bounds of this range by adding and subtracting the standard deviation (7.3) from the mean (70.8).
02

Calculating values for 95% data

Similarly, about 95% of the data falls within 2 standard deviations of the mean. Calculate the upper and lower bounds of this range by adding and subtracting twice the standard deviation from the mean.
03

Measuring the Unusualness of 54 million BTU

Comparing the given value of 54 million BTU with the calculated ranges. If the value lies beyond 2 standard deviations from the mean, it can be said that the value is unusual.
04

Assessing The Energy Consumption of Indiana

The same logic will be applied to the given data for Indiana, which is 80.5 million BTU. If it sits beyond 2 standard deviations, it's considered unusually high.

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