816
TURNER
For certain statistical treatments involving such distributions, a
data transformation may be desirable. However, the most important
feature of distributions skewed to the high side is that the number of
individuals -exceeding the mean is greater than expected in a normal
distribution of the same mean and variance. For example, it has been
pointed out that, with the data of Turekian and Kulp to fix the standard
deviation and with the assumption of a mean "Sr level of 10 pce *Sr/g
Ca for the population, the percentage of the population exceeding twice
the mean is 0.6 for a normaldistribution and 5 for a lognormal distribution,*® Table 7 shows a similar comparison taken from Neuman.°
Table 7— NUMBER OF PEOPLE EXPECTED TO HAVE “Sr BONE
BURDENS EXCEEDING 100 PC %Sr/G Ca, ASSUMING NORMAL
AND LOGNORMAL DISTRIBUTIONS OF Sr IN THE WORLD
POPU LATION*
Average Sr
Number of people
in world population,
pe Sr/g Ca
Normal distribution
Lognormal distribution
50
3,000,000
100,000 ,000
35
1,000
8,000,000
25
100,000
*From W. F. Neuman, Bull. Atomic Scient., 14: 31-34 (1958).
The observations and theoretical predictions regarding 1317 which
are set forth in this paper are consistent with the recommendation of
the Federal Radiation Council. Snyder and Cook**:*4 have also adduced
support for this assumption. However, the probability of individuals
exceeding three times the population mean is apparently by no means
as remote as stated by Libby: “...at steady state among people living
in a given locality only one person in about 700 will have more than
twice the average Sr” burden,
and the chances of anyone having as
much as three times the normal burden will be about one in twenty
million.’
Why do non-Gaussian distributions arise? Are they simply a re-
flection of diet? Clearly, levels of radionuclides in consumers must
be generally correlated with intake.
We do not expect to find high
levels of “Sr in areas where foods are knownto be low in "Sr, or
vice versa, However, to say that high levels of dietary Sr are asso-~
ciated with high levels of bone Sr implies nothing about the influence,
if any, of the frequency distribution of *Sr in a large numberofindi-
vidual diets on the frequency distribution of “Sr in the bones of the
consumers of these diets.
This problem has been approached theoretically by means of the
probabilistic model described above. It will be recalled that the dis-