In some locations, radiation levels in homes are measured at well above normal background levels in the environment. As a result, many architects and builders are making design changes to ensure adequate air exchange so that radiation will not be "trapped" in homes. In one such location, 50 homes, levels were measured, and the mean level was 10 parts per billion (ppb), the median was 8 ppb, and the standard deviation was 3 ppb. Background levels in this location are at about 4 ppb.
a. Based on these results, is the distribution of the 50 homes' radiation levels symmetric, skewed to the left, skewed to the right? Why?
b. Use both Chebyshev's Rule to and the Empirical Rule to describe the distribution of radiation levels. Which do you think is most appropriate in this case? Why?
c. Use the results from part b to approximate the number of homes in this sample that have radiation levels above the background level.
d. Suppose another home is measured at a location 10 miles from the one sampled and has a level of 20 ppb. What is the z-score for this measurement relative to the 50 homes sampled in the other location? Is it likely that this new measurement comes from the same distribution of radiation levels as the other 50? Why? How would you go about confirming your conclusion?