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 8ppb and the standard deviation
was 3ppb. Background levels in this location are at about 4ppb.
(i) Based on these results, is the distribution of the 50 homes' radiation
levels symmetric, skewed to the left or skewed to the right? Why?
(ii) Use both the Chebyshev's Rule and the Empirical Rule to describe
the distribution of radiation levels. Which do you think is most
appropriate in this case? Why?
(iii) Use the results from part (ii) to approximate the number of homes in
this sample that have radiation levels above the background level.
(iv) Suppose another home is measured at a location 10 miles from the
one sampled and has a level of 20ppb. Is it likely that this new
measurement comes from the same distribution of radiation levels
as the other 50? How would you go about confirming your