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In statistics, the 68–95–99.7 rule, also known as the empirical rule, and sometimes abbreviated 3sr, is a shorthand used to remember the percentage of values that lie within an interval estimate in a normal distribution: approximately 68%, 95%, and 99.7% of the values lie within one, two, and three standard deviations of the mean, respectively.
Hawke v. Smith, 253 U.S. 221 (1920): "[Article V] makes provision for the proposal of amendments either by two-thirds of both houses of Congress or on application of the legislatures of two-thirds of the states, thus securing deliberation and consideration before any change can be proposed. The proposed change can only become effective by the ...
A two-thirds supermajority in the Senate is 67 out of 100 senators, while a two-thirds supermajority in the House is 290 out of 435 representatives. However, since many votes take place without every seat in the House filled and representatives participating, it does not often require 67 senators or 290 representatives to achieve this ...
The rule can then be derived [2] either from the Poisson approximation to the binomial distribution, or from the formula (1−p) n for the probability of zero events in the binomial distribution. In the latter case, the edge of the confidence interval is given by Pr( X = 0) = 0.05 and hence (1− p ) n = .05 so n ln (1– p ) = ln .05 ≈ −2.996.
Level 1 players would assume that everyone else was playing at level 0, responding to an assumed average of 50 in relation to naive play, and thus their guess would be 33 (2/3 of 50). At k-level 2, a player would play more sophisticatedly and assume that all other players are playing at k-level 1, so they would choose 22 (2/3 of 33). [9]
Elections with notable third party electoral performances (1900–present) [12] State Gubernatorial elections Senate elections Total elections Threshold reached
English style guides prescribe writing the percent sign following the number without any space between (e.g. 50%). [sources 1] However, the International System of Units and ISO 31-0 standard prescribe a space between the number and percent sign, [8] [9] [10] in line with the general practice of using a non-breaking space between a numerical value and its corresponding unit of measurement.
In some cases, the required percentage of member states in favor is increased to 72%. [9] A "supermajority" is a specified threshold greater than one half. [6] A common use of a supermajority is a "two-thirds vote", which is sometimes referred to as a "two-thirds majority".