# Sampling Distribution of Proportion

Definition: The Sampling Distribution of Proportion measures the proportion of success, i.e. a chance of occurrence of certain events, by dividing the number of successes i.e. chances by the sample size ’n’. Thus, the sample proportion is defined as p = x/n.

The sampling distribution of proportion obeys the binomial probability law if the random sample of ‘n’ is obtained with replacement. Such as, if the population is infinite and the probability of occurrence of an event is π’, then the probability of non-occurrence of the event is (1-π).  Now consider all the possible sample size ‘n’ drawn from the population and estimate the proportion ‘p’ of success for each. Then the mean (?p) and the standard deviation (σp) of the sampling distribution of proportion can be obtained as:

?
p = mean of proportion
π = population proportion which is defined as π = X/N, where X is the number of elements that possess a certain characteristic and N is the total number of items in the population.
σp = standard error of proportion that measures the success (chance) variations of sample proportions from sample to sample
n= sample size, If the sample size is large (n≥30), then the sampling distribution of proportion is likely to be normally distributed.

The following formula is used when population is finite, and the sampling is made without the replacement:

## Related pages

subsistence wage theorylearned needs theory of motivationdiminishing marginal utility examplemeaning of fmcgmonopolistic definelpp formulationcompensation planning in hrmlinear programing simplex methodeducation loan moratorium periodjane moutonformal and informal groupswhy indifference curve is convex to the origincontent and process theories of motivationnational pension yojanacrr meaningquota samplingmcclelland's achievement need theoryorganisational hierarchy definitionchannel conflict resolutiondeflationary fiscal policy definitionexpentancy theorymeaning of corporate ethicssampling plan definitiondefine resonancesexplain fiscal deficitcorporate culture tutor2uhow do you calculate inventory turnover ratioexposure in hindiivan pavlov theory of classical conditioningelasticity of factor substitutionretained profit advantagesdiminishing marginal utilityquants meaningbusiness process reengineering frameworkautonomous multiplierprovidend fund indiarationing defineimportance of oligopolyexample of id ego superegodefinition holisticallywhat defines a monopolyconglomerate merger definitionabc method of inventoryencirclement strategydefine geocentric approachintrapreneurship definitiondeontological definitionimportance of industrial relations pptcosting methods for pricingmanpower planning procedurewhat are the four quadrants of the johari windowexplain stratified samplingexport factoring definitionthe equity theory of motivationallport common traitscarrot and stick method of motivationquestioner definechannel conflict in marketingpoaching staffhow to calculate fixed asset turnoverfeatures of an oligopoly marketcash reserve ratiodetermination meaning in telugucomputerised meaningmcclelland three needs theorydelphi technique definitionmarketing 4p definitionbusiness process reengineering bpradvantages of vestibule trainingexamples of sociocultural factorsadvantages and disadvantages of polycentric approachcharacteristics of monopolistic market structurepolycentric approachexternal commercial borrowings ecbwhat is an indifference mapintersecting lines definedeclining marginal utilityjob enrichment meaningmeaning of equity finance