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Includes key identities such as union/intersection probabilities, standardize-to-test-statistic forms, confidence-interval structure, chi-square statistic, and regression sampling components. Provides organized tables for distribution moments and standard errors, plus standardized sampling results for proportions and means. Ends with a Standard normal (z) probability table entry guide.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/ap-statistics-2020-formulas-and-tables-sheet-statistical-formulas-probability-distributions-sampling-distributions-and-z-table/266543/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/ap-statistics-2020-formulas-and-tables-sheet-statistical-formulas-probability-distributions-sampling-distributions-and-z-table/266543.png","ImageObject",300,407,{"name":92,"@type":93},"Levi","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-03","2026-09-14",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",17,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What formulas are included for descriptive statistics in this sheet?","Question",{"text":113,"@type":114},"The sheet lists standard descriptive statistics relationships, including summation forms tied to mean and regression components, alongside correlation/regression-related expressions.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"Which probability and distribution results are provided?",{"text":118,"@type":114},"It provides probability rules for unions and intersections and conditional probability, plus a reference table with mean and standard deviation formulas for discrete distributions such as binomial and geometric.",{"name":120,"@type":111,"acceptedAnswer":121},"How does the sheet support inferential statistics like confidence intervals and test statistics?",{"text":122,"@type":114},"It specifies the confidence interval structure using a statistic plus or minus a critical value times a standard error, and it includes a chi-square statistic form and standardized test-statistic context. It also includes the standard normal z probability table for looking up tail areas.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},266543,1789408823,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":29,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":130,"read_time":144,"preview_page_count":4},7971461740909,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","Formulas and Tables for AP Statistics  \nI. Descriptive Statistics x~~ ~~ = 1n~~ ~~ ∑ xi = ∑nxi~~  ~~ = a + bx  \nr = n~~ ~~~~ ~~1 ∑ 􀂧􀂩􀂨 xi~~ ~~s−x~~ ~~x~~  ~~ 􀂷􀂹􀂸 􀂧􀂩􀂨 yi~~ ~~s−y~~ ~~y~~ ~~􀂷􀂹􀂸 II. Probability and Distributions  \nP ( A ∪ B ) = P ( A) + P( B ) − P( A ∩ B )  \nsx = ~~ ~~n~~ ~~~~ ~~1 ∑ ( xi − x~~ ~~ )2 = ∑~~ ~~(~~ ~~xni~~ ~~1x~~ ~~)2~~  ~~y = a + bx  \nb = r ~~ ~~ssy~~ ~~  \nx  \nP ( A | B ) = P~~ ~~(AP~~(~~∩B~~)~~B~~ ~~)  \n\n| Probability Distribution | Mean | Standard Deviation |\n| --- | --- | --- |\n| Discrete random variable, X | µX = E ( X ) = ∑ xiP ( xi ) | σX = ∑ ( xi − µX )2 P ( xi ) |\n| If 􀜺 has a binomial distribution with parameters n and p, then:\u003Cbr>P ( X = x ) = 􀂨􀂧􀂩nx􀂷􀂹􀂸 px ( 1 − p )n − x where x = 0, 1, 2, 3, 􀀡 , n | µX = np | σX = np ( 1 − p ) |\n| If 􀜺 has a geometric distribution with parameter p, then:\u003Cbr>P ( X = x ) = ( 1 − p )x −1 p where x = 1, 2, 3, 􀀡 | µX = 1p |  1 − p σ =\u003Cbr>X p |\n\nIII. Sampling Distributions and Inferential Statistics  \n\n| Standardized test statistic: ~~ ~~stanstatidardstic~~ ~~−~~ ~~paerror~~ ~~ofrtameterhe~~ ~~statistic |\n| --- |\n| Confidence interval: statistic ± ( critical value )( standard error of statistic) |\n\nChi-square statistic: χ 2 = ∑ ~~ ~~(~~ ~~observedexp−~~ ~~expectedected~~ ~~)2~~ ~~  \nAP Statistics 2020 Formulas and Tables Sheet  \nIII. Sampling Distributions and Inferential Statistics (continued) Sampling distributions for proportions:  \n\n| Random\u003Cbr>Variable | Parameters of\u003Cbr>Sampling Distribution |  |  |  | Standard Error* of Sample Statistic |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- |\n| For one population:\u003Cbr>ˆ\u003Cbr>p | µ = p | σ = |  | | s = |  | |\n| For two populations:\u003Cbr>1 − 2 | µ1 − 2 = p1 − p2 | σ1 − 2 = | \u003Cbr>p1 ( 1 − p1 ) p2 ( )\u003Cbr>+ n 1\u003Cbr>1 − p2\u003Cbr>n 2 |  | s1 − 2 = | |  |\n|  |  |  |  |  | When p1 = p2 is assumed:\u003Cbr>s1 − 2 = c ( 1 − c ) 􀂨􀂧􀂩 ~~ ~~1n1 + ~~ ~~1n2~~ ~~􀂷􀂹􀂸 where c = Xn11~~ ~~~~ ~~Xn22 |  |  |\n\nSampling distributions for means:  \n\n| Random\u003Cbr>Variable | Parameters of Sampling Distribution |  | Standard Error* of Sample Statistic |  |\n| --- | --- | --- | --- | --- |\n| For one population:\u003Cbr>X | µX = µ | σ   =  σ \u003Cbr>X\u003Cbr>~~ ~~ n\u003Cbr>| s   =  s  X\u003Cbr>~~ ~~ n\u003Cbr>|  |\n| For two populations:\u003Cbr>X − X\u003Cbr>1 2 | µX − X = µ1 − µ2 1 2 | σ =\u003Cbr>X − X\u003Cbr>1 2\u003Cbr>2 σ\u003Cbr>1\u003Cbr>n 1\u003Cbr>+\u003Cbr>2 σ\u003Cbr>2\u003Cbr>n 2\u003Cbr>| s ~~ ~~ ~~ ~~ = X − X\u003Cbr>1 2 | |\n\nSampling distributions for simple linear regression:  \n\n| Random\u003Cbr>Variable | Parameters of Sampling Distribution |  |  | Standard Error* of Sample Statistic |  |\n| --- | --- | --- | --- | --- | --- |\n| For slope: b | µ = β b | σ =  σ \u003Cbr>b ,\u003Cbr>σ ~~ ~~ nx\u003Cbr>|  | where\u003Cbr>s =  s \u003Cbr>b ,\u003Cbr>s  n − 1\u003Cbr>x\u003Cbr> ∑ ( yi − i )2  s =\u003Cbr>−\u003Cbr>\u003Cbr>\u003Cbr>n 2 |  |\n|  |  | where σ =\u003Cbr>x | |  |  |\n|  |  |  |  | and s = x | |\n\n*Standard deviation is a measurement of variability from the theoretical population. Standard error is the estimate of the standard deviation. If the standard deviation of the statistic is assumed to be known, then the standard deviation should be used instead of the standard error.  \nAP Statistics 2020 Formulas and Tables Sheet  \nTable entry for z is the probability lying below z.  \nProbability  \nz  \nTable A Standard normal probabilities  \nz  \n-3.4 -3.3 -3.2 -3.1 -3.0 -2.9 -2.8 -2.7 -2.6 -2.5 -2.4 -2.3 -2.2 -2.1 -2.0 -1.9 -1.8 -1.7 -1.6 -1.5 -1.4 -1.3 -1.2 -1.1 -1.0 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1  \n-0.0  \n.00  \n.0003 .0005 .0007 .0010 .0013 .0019 .0026 .0035 .0047 .0062 .0082 .0107 .0139 .0179 .0228 .0287 .0359 .0446 .0548 .0668 .0808 .0968 .1151 .1357 .1587 .1841 .2119 .2420 .2743 .3085 .3446 .3821 .4207 .4602  \n.5000  \n.01  \n.0003 .0005 .0007 .0009 .0013 .0018 .0025 .0034 .0045 .0060 .0080 .0104 .0136 .0174 .0222 .0281 .0351 .0436 .0537 .0655 .0793 .0951 .1131 .1335 .1562 .1814 .2090 .2389 .2709 .3050 .3409 .3783 .4168 .4562  \n.4960  \n.02  \n.0003 .0005 .0006 .0009 .0013 .0018 .0024 .0033 .0044 .0059 .0078 .0102 .0132 .0170 .0217 .0274 .0344 .0427 .0526 .0643 .0778 .0934 .1112 .131","cbCaig5E23Qos5Fh","https://ap.wps.com/l/cbCaig5E23Qos5Fh","pdf",1024393,"English","# Descriptive Statistics\n# Probability and Distributions\n## Probability identities and conditional probability\n## Mean and standard deviation formulas for common distributions\n# Sampling Distributions and Inferential Statistics\n## Sampling distributions for proportions\n## Sampling distributions for means\n## Sampling distributions for simple linear regression\n## Confidence intervals and test statistics\n# Standard Normal z-Table (Table A)","[{\"question\":\"What formulas are included for descriptive statistics in this sheet?\",\"answer\":\"The sheet lists standard descriptive statistics relationships, including summation forms tied to mean and regression components, alongside correlation/regression-related expressions.\"},{\"question\":\"Which probability and distribution results are provided?\",\"answer\":\"It provides probability rules for unions and intersections and conditional probability, plus a reference table with mean and standard deviation formulas for discrete distributions such as binomial and geometric.\"},{\"question\":\"How does the sheet support inferential statistics like confidence intervals and test statistics?\",\"answer\":\"It specifies the confidence interval structure using a statistic plus or minus a critical value times a standard error, and it includes a chi-square statistic form and standardized test-statistic context. It also includes the standard normal z probability table for looking up tail areas.\"}]","AP Statistics 2020 Formulas and Tables Sheet - Statistical formulas, probability distributions, sampling distributions and z-table | PDF",15]