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

Author

Zacariaz Martinez, Apr 11 2013

Keywords

• nonn

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.

Examples

			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.
		

References

• F. Reif, Fundamentals of Statistical and Thermal Physics, McGraw-Hill, 1965

Crossrefs

Cf. A002162, A014088, A033810, A050255.

Programs

PARI

a(n)=ceil((log(2))/(log(10^n/(10^n-1)))); \\ Joerg Arndt, Apr 15 2013

Formula

a(n) = ceiling((log(2))/(log(10^n/(10^n-1)))).