login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A239385 Decimal expansion of the probability of a normal-error variable exceeding the mean by more than four standard deviations. 7
3, 1, 6, 7, 1, 2, 4, 1, 8, 3, 3, 1, 1, 9, 9, 2, 1, 2, 5, 3, 7, 7, 0, 7, 5, 6, 7, 2, 2, 1, 5, 1, 2, 9, 8, 4, 4, 3, 8, 3, 3, 3, 7, 5, 4, 8, 0, 2, 7, 6, 5, 0, 8, 5, 4, 9, 3, 3, 1, 7, 2, 2, 0, 7, 8, 5, 8, 5, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

-4,1

COMMENTS

The probability P{(x-m)/s > 4} for a normally distributed random variable x with mean m and standard deviation s.

In experimental sciences (hypothesis testing), a measured excursion exceeding background "noise" by more than four standard deviations is considered significant, unless it is an isolated case among thousands of iterated measurements.

LINKS

Stanislav Sykora, Table of n, a(n) for n = -4..1996

Wikipedia, Normal distribution

FORMULA

P{(x-m)/s > 4} = P{(x-m)/s < -4} = 0.5*erfc(4/sqrt(2)) = erfc(2*sqrt(2))/2, with erfc(x) being the complementary error function.

EXAMPLE

0.000031671241833119921253770756722151298443833375480276508549331722...

PROG

(PARI) n=4; a=0.5*erfc(n/sqrt(2))  \\ Use sufficient realprecision

CROSSREFS

Cf. P{(x-m)/s>n}: A239382 (n=1), A239383 (n=2), A239384 (n=3), A239386 (n=5), A239387 (n=6).

Sequence in context: A242729 A112692 A198614 * A124929 A208766 A259454

Adjacent sequences:  A239382 A239383 A239384 * A239386 A239387 A239388

KEYWORD

nonn,cons

AUTHOR

Stanislav Sykora, Mar 18 2014

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified March 29 21:48 EDT 2017. Contains 284288 sequences.