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...

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

Links

Table of n, a(n) for n=1..20.

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

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