

A219330


Number of random selections (with replacement) needed from a normal population to assure a greater than onehalf 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
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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, McGrawHill, 1965


LINKS

Table of n, a(n) for n=1..20.
http://mathworld.wolfram.com/MarkovChain.html, http://www.thethousand.com, http://mathworld.wolfram.com/Quantile.html


FORMULA

a(n) = least integer function of [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.


MATHEMATICA

ceiling((log(2))/(log(10^n/(10^n1))))


PROG

(PARI) a(n)=ceil((log(2))/(log(10^n/(10^n1)))); \\ Joerg Arndt, Apr 15 2013


CROSSREFS

Cf. A002162, A014088, A033810, A050255.
Sequence in context: A197525 A133697 A224758 * A122010 A180911 A084774
Adjacent sequences: A219327 A219328 A219329 * A219331 A219332 A219333


KEYWORD

nonn


AUTHOR

Zacariaz Martinez, Apr 11 2013


STATUS

approved



