# Question

The paper “Conditional Simulation of Waste-Site Performance”[Technometrics (1994) 36: 129–161] discusses the evaluation of a pilot facility for demonstrating the safe management, storage, and disposal of defense-generated, radioactive, transuranic waste. Researchers have deter-mined that one potential pathway for release of radionuclides is through contaminant transport in groundwater. Recent focus has been on the analysis of transmissivity, a function of the properties and the thickness of an aquifer that reflects the rate at which water is transmitted through the aquifer. The following table contains 41 measurements of transmissivity, T, made at the pilot facility.

a. Draw a relative frequency histogram for the 41 values of T.

b. Describe the shape of the histogram.

c. When the relative frequency histogram is highly skewed to the right, the Empirical Rule may not yield very accurate results. Verify this statement for the data given.

d. Data analysts often find it easier to work with mound-shaped relative frequency histograms. A transformation of the data will sometimes achieve this shape. Replace the given 41 T values with the logarithm base 10 of the values and reconstruct the relative frequency histogram. Is the shape more mound-shaped than the original data? Apply the Empirical Rule to the transformed data, and verify that it yields more accurate results than it did with the original data.

a. Draw a relative frequency histogram for the 41 values of T.

b. Describe the shape of the histogram.

c. When the relative frequency histogram is highly skewed to the right, the Empirical Rule may not yield very accurate results. Verify this statement for the data given.

d. Data analysts often find it easier to work with mound-shaped relative frequency histograms. A transformation of the data will sometimes achieve this shape. Replace the given 41 T values with the logarithm base 10 of the values and reconstruct the relative frequency histogram. Is the shape more mound-shaped than the original data? Apply the Empirical Rule to the transformed data, and verify that it yields more accurate results than it did with the original data.

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