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A219330
Number of random selections (with replacement) needed from a normal population to assure a greater than one-half chance that the selected group contains the top 10th percentile individual, top 1st percentile individual, the 0.1 percentile, 0.01 percentile etc...
0
7, 69, 693, 6932, 69315, 693147, 6931472, 69314718, 693147181, 6931471806, 69314718056, 693147180560, 6931471805600, 69314718055995, 693147180559945, 6931471805599453, 69314718055994531, 693147180559945310, 6931471805599453094, 69314718055994530942
OFFSET
1,1
COMMENTS
a(n) is the least number of random selections (with replacement) required that assures a group having at least a 0.5 probability of containing the top 100/(10^n)th percentile individual. Converges toward log(2)*10^n with increasing n.
REFERENCES
F. Reif, Fundamentals of Statistical and Thermal Physics, McGraw-Hill, 1965
FORMULA
a(n) = ceiling((log(2))/(log(10^n/(10^n-1)))).
EXAMPLE
To assure a greater than 1/2 chance of finding an individual with, say, an IQ in the top one out of a thousand or 1/(10^3), you must select at least (with replacement) a(3) = 693 individuals.
PROG
(PARI) a(n)=ceil((log(2))/(log(10^n/(10^n-1)))); \\ Joerg Arndt, Apr 15 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Zacariaz Martinez, Apr 11 2013
STATUS
approved