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Some comments on George's "adding together 14 numbers, each varying
randomly in the range between -.05' and +.05' ", in [NavList 1433]. 

As the variation in each number is due to rounding error, we can assume
a uniform distribution for each variable. The standard deviation of a
uniform distribution is the interval length divided by sqrt(12), i.e. in
this case 0.1'/sqrt(12)=0.03'. Adding 14 such distributions results in a
nearly normal distribution with standard deviation 0.03'*sqrt(14)=0.1'. 

In such a normal distribution, the probability of an error in excess of
0.19' is 6%, and 68% for an error less than 0.1'. This corresponds
pretty well with George's brute-force simulations, as it should.

With Frank's assumed distance measurements within 0.1', no timing errors
and presumably negligible almanac data errors, furthermore assuming a
"good cut" between the lines; we get a resulting standard deviation of
say 0.08'. Using a "positional error multiplier" of 60 gives us a "less
than 6 miles error" with about 80% probability, less than 9 miles with
95%. So I think Frank's claim is reasonable, given the stated
preconditions. 

Frank could also claim that although there is 20% probability to have an
error above 6 miles, there is as well a 20% probability that the error
is less than 1.2 miles!

Lars
59N 18E



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