approximate a logarithmic sequence to the base 2.)

The mean and standard

deviation of In 8.5, 1n 57.3, and In 278 are 3.9387 + 1.7464.
To estimate the magnitude of a "reasonable estimate” based on these three

measurements, the log mean and standard deviation were used to generate
a synthetic sample (n = 500) of Ts:
The individual values based on

In I, = 3.9387 + 1.7464 ranged from 2 g/day to 3,575 g/day; the overall

mean (n = 500) was 213 + 609 g/day.

Plutonium Concentrations in Vegetation and Soil
The concentrations of plutonium (pCi/g) in vegetation and soil samples
collected from Area 13 are listed in Tables 1 and 2.
The areas of
sampling strata are given in Table 3.
The arithmetic (normal) and
geometric (lognormal) estimates of population parameters for each sampling stratum are given in Table 4.
The raw data of Tables 1 and 2 and their natural logarithms were used to
construct normalized histograms in which the cell width on the horizontal

axis is_determined by z = (x-xg)/sg, where x is the limit between two

cells, xg is the mean, and sg is the standard deviation of the sample
set.
The vertical height of the cell is the number of variates (frequency of observations) that fall in the cell interval divided by the

total number of variates (n) in the sample.

To facilitate comparison, a

normal curve, i.e., ¢(z) = (s(2m)1/2)-1 exp (-1/2 22), was sketched on
the same coordinates.

The histogram (not shown) for c,1,2), the concentrations (Table 1) of

plutonium in vegetation samples from strata 1 and 2, was sharply skewed
to the right, suggesting a lognormal distribution, while the histogram
of ln c.1,2) was sharply skewed to the left, suggesting a truncated
lognormal distribution. Maps of Area 13 sampling strata (see the article
by Delfiner, and Gilbert, this volume) show that parts of strata 1 and 2
extend beyond the fenced area and were not sampled.
In other words, the
apparently truncated distribution curve appears to be a true reflection
of the actual situation.
The histogram of In Cc(1-5), Figure 2,

is not perfectly symmetrical, but

the observed cell counts (5, 17, 35, 21, 17, 9) are close to the counts
expected for a normal curve (5.3, 16.5, 29, 29, 16.5, 5.3). A chi square
test, comparing the observed and expected cell counts, indicated x2 =
3.1547 and P(x2) = 0.3239.
As P(x2)> 0.95 is required for rejection of
the null hypothesis, the test provides no basis for rejecting the hypothesis that the observed frequency distribution is lognormal.
The
same procedure was followed in constructing and testing all the histograms shown in Figures 1 through 8.
In no case did the chi square test
indicate that rejection of the null hypothesis was required.

Based on the results displayed in Figures 2, 3, 4, and 5, it was assumed
that Cy and C_ are lognormally distributed in each of the six sampling
strata of the inner compound.
The population parameters for each sam-

pling stratum (xg and sg) are given in Table 4.

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