표준정규분포표

**표준정규분포표**(standard normal table)accessdate=21 December 2018는 정규 분포의 누적 분포 함수 값인 Φ 값에 대한 표이다. 통계가 표준 정규 분포의 값 아래, 또는 위 값 사이에서 그리고 확장하여 모든 정규 분포에서 관찰 될 확률을 찾는 데 사용된다. 무한한 다양한 정규 분포가 있기 때문에 모든 정규 분포에 대해 확률 테이블을 인쇄 할 수 없기 때문에 정규 분포를 표준 정규로 변환한 다음 표준 정규분포표를 사용하여 확률을 찾는 것이 일반적이다.page=214
# 표준정규분포표
z보다 작을 값을 가질 확률에 대한 누적 표준정규분포표는 다음과 같다.Z Table Statistics and Chart {| class="wikitable" ! *z* !! − 0.00!! − 0.01!! − 0.02!! − 0.03!! − 0.04!! − 0.05!! − 0.06!! − 0.07!! − 0.08!! − 0.09 |- ! -4.0 |0.00003||0.00003||0.00003||0.00003||0.00003||0.00003||0.00002||0.00002||0.00002||0.00002 |- | colspan="11" | |- ! -3.9 |0.00005||0.00005||0.00004||0.00004||0.00004||0.00004||0.00004||0.00004||0.00003||0.00003 |- ! -3.8 |0.00007||0.00007||0.00007||0.00006||0.00006||0.00006||0.00006||0.00005||0.00005||0.00005 |- ! -3.7 |0.00011||0.00010||0.00010||0.00010||0.00009||0.00009||0.00008||0.00008||0.00008||0.00008 |- ! -3.6 |0.00016||0.00015||0.00015||0.00014||0.00014||0.00013||0.00013||0.00012||0.00012||0.00011 |- ! -3.5 |0.00023||0.00022||0.00022||0.00021||0.00020||0.00019||0.00019||0.00018||0.00017||0.00017 |- | colspan="11" | |- ! -3.4 |0.00034||0.00032||0.00031||0.00030||0.00029||0.00028||0.00027||0.00026||0.00025||0.00024 |- ! -3.3 |0.00048||0.00047||0.00045||0.00043||0.00042||0.00040||0.00039||0.00038||0.00036||0.00035 |- ! -3.2 |0.00069||0.00066||0.00064||0.00062||0.00060||0.00058||0.00056||0.00054||0.00052||0.00050 |- ! -3.1 |0.00097||0.00094||0.00090||0.00087||0.00084||0.00082||0.00079||0.00076||0.00074||0.00071 |- ! -3.0 |0.00135||0.00131||0.00126||0.00122||0.00118||0.00114||0.00111||0.00107||0.00104||0.00100 |- | colspan="11" | |- ! -2.9 |0.00187||0.00181||0.00175||0.00169||0.00164||0.00159||0.00154||0.00149||0.00144||0.00139 |- ! -2.8 |0.00256||0.00248||0.00240||0.00233||0.00226||0.00219||0.00212||0.00205||0.00199||0.00193 |- ! -2.7 |0.00347||0.00336||0.00326||0.00317||0.00307||0.00298||0.00289||0.00280||0.00272||0.00264 |- ! -2.6 |0.00466||0.00453||0.00440||0.00427||0.00415||0.00402||0.00391||0.00379||0.00368||0.00357 |- ! -2.5 |0.00621||0.00604||0.00587||0.00570||0.00554||0.00539||0.00523||0.00508||0.00494||0.00480 |- | colspan="11" | |- ! -2.4 |0.00820||0.00798||0.00776||0.00755||0.00734||0.00714||0.00695||0.00676||0.00657||0.00639 |- ! -2.3 |0.01072||0.01044||0.01017||0.00990||0.00964||0.00939||0.00914||0.00889||0.00866||0.00842 |- ! -2.2 |0.01390||0.01355||0.01321||0.01287||0.01255||0.01222||0.01191||0.01160||0.01130||0.01101 |- ! -2.1 |0.01786||0.01743||0.01700||0.01659||0.01618||0.01578||0.01539||0.01500||0.01463||0.01426 |- ! -2.0 |0.02275||0.02222||0.02169||0.02118||0.02068||0.02018||0.01970||0.01923||0.01876||0.01831 |- | colspan="11" | |- ! -1.9 |0.02872||0.02807||0.02743||0.02680||0.02619||0.02559||0.02500||0.02442||0.02385||0.02330 |- ! -1.8 |0.03593||0.03515||0.03438||0.03362||0.03288||0.03216||0.03144||0.03074||0.03005||0.02938 |- ! -1.7 |0.04457||0.04363||0.04272||0.04182||0.04093||0.04006||0.03920||0.03836||0.03754||0.03673 |- ! -1.6 |0.05480||0.05370||0.05262||0.05155||0.05050||0.04947||0.04846||0.04746||0.04648||0.04551 |- ! -1.5 |0.06681||0.06552||0.06426||0.06301||0.06178||0.06057||0.05938||0.05821||0.05705||0.05592 |- | colspan="11" | |- ! -1.4 |0.08076||0.07927||0.07780||0.07636||0.07493||0.07353||0.07215||0.07078||0.06944||0.06811 |- ! -1.3 |0.09680||0.09510||0.09342||0.09176||0.09012||0.08851||0.08692||0.08534||0.08379||0.08226 |- ! -1.2 |0.11507||0.11314||0.11123||0.10935||0.10749||0.10565||0.10383||0.10204||0.10027||0.09853 |- ! -1.1 |0.13567||0.13350||0.13136||0.12924||0.12714||0.12507||0.12302||0.12100||0.11900||0.11702 |- ! -1.0 |0.15866||0.15625||0.15386||0.15151||0.14917||0.14686||0.14457||0.14231||0.14007||0.13786 |- | colspan="11" | |- ! -0.9 |0.18406||0.18141||0.17879||0.17619||0.17361||0.17106||0.16853||0.16602||0.16354||0.16109 |- ! -0.8 |0.21186||0.20897||0.20611||0.20327||0.20045||0.19766||0.19489||0.19215||0.18943||0.18673 |- ! -0.7 |0.24196||0.23885||0.23576||0.23270||0.22965||0.22663||0.22363||0.22065||0.21770||0.21476 |- ! -0.6 |0.27425||0.27093||0.26763||0.26435||0.26109||0.25785||0.25463||0.25143||0.24825||0.24510 |- ! -0.5 |0.30854||0.30503||0.30153||0.29806||0.29460||0.29116||0.28774||0.28434||0.28096||0.27760 |- | colspan="11" | |- ! -0.4 |0.34458||0.34090||0.33724||0.33360||0.32997||0.32636||0.32276||0.31918||0.31561||0.31207 |- ! -0.3 |0.38209||0.37828||0.37448||0.37070||0.36693||0.36317||0.35942||0.35569||0.35197||0.34827 |- ! -0.2 |0.42074||0.41683||0.41294||0.40905||0.40517||0.40129||0.39743||0.39358||0.38974||0.38591 |- ! -0.1 |0.46017||0.45620||0.45224||0.44828||0.44433||0.44038||0.43644||0.43251||0.42858||0.42465 |- ! -0.0 |0.50000||0.49601||0.49202||0.48803||0.48405||0.48006||0.47608||0.47210||0.46812||0.46414 |- ! *z* !! − 0.00!! − 0.01!! − 0.02!! − 0.03!! − 0.04!! − 0.05!! − 0.06!! − 0.07!! − 0.08!! − 0.09 |} {| class="wikitable" ! *z* !! + 0.00!! + 0.01!! + 0.02!! + 0.03!! + 0.04!! + 0.05!! + 0.06!! + 0.07!! + 0.08!! + 0.09 |- ! 0.0 |0.50000||0.50399||0.50798||0.51197||0.51595||0.51994||0.52392||0.52790||0.53188||0.53586 |- ! 0.1 |0.53983||0.54380||0.54776||0.55172||0.55567||0.55962||0.56360||0.56749||0.57142||0.57535 |- ! 0.2 |0.57926||0.58317||0.58706||0.59095||0.59483||0.59871||0.60257||0.60642||0.61026||0.61409 |- ! 0.3 |0.61791||0.62172||0.62552||0.62930||0.63307||0.63683||0.64058||0.64431||0.64803||0.65173 |- ! 0.4 |0.65542||0.65910||0.66276||0.66640||0.67003||0.67364||0.67724||0.68082||0.68439||0.68793 |- | colspan="1" | |- ! 0.5 |0.69146||0.69497||0.69847||0.70194||0.70540||0.70884||0.71226||0.71566||0.71904||0.72240 |- ! 0.6 |0.72575||0.72907||0.73237||0.73565||0.73891||0.74215||0.74537||0.74857||0.75175||0.75490 |- ! 0.7 |0.75804||0.76115||0.76424||0.76730||0.77035||0.77337||0.77637||0.77935||0.78230||0.78524 |- ! 0.8 |0.78814||0.79103||0.79389||0.79673||0.79955||0.80234||0.80511||0.80785||0.81057||0.81327 |- ! 0.9 |0.81594||0.81859||0.82121||0.82381||0.82639||0.82894||0.83147||0.83398||0.83646||0.83891 |- | colspan="1" | |- ! 1.0 |0.84134||0.84375||0.84614||0.84849||0.85083||0.85314||0.85543||0.85769||0.85993||0.86214 |- ! 1.1 |0.86433||0.86650||0.86864||0.87076||0.87286||0.87493||0.87698||0.87900||0.88100||0.88298 |- ! 1.2 |0.88493||0.88686||0.88877||0.89065||0.89251||0.89435||0.89617||0.89796||0.89973||0.90147 |- ! 1.3 |0.90320||0.90490||0.90658||0.90824||0.90988||0.91149||0.91308||0.91466||0.91621||0.91774 |- ! 1.4 |0.91924||0.92073||0.92220||0.92364||0.92507||0.92647||0.92785||0.92922||0.93056||0.93189 |- | colspan="1" | |- ! 1.5 |0.93319||0.93448||0.93574||0.93699||0.93822||0.93943||0.94062||0.94179||0.94295||0.94408 |- ! 1.6 |0.94520||0.94630||0.94738||0.94845||0.94950||0.95053||0.95154||0.95254||0.95352||0.95449 |- ! 1.7 |0.95543||0.95637||0.95728||0.95818||0.95907||0.95994||0.96080||0.96164||0.96246||0.96327 |- ! 1.8 |0.96407||0.96485||0.96562||0.96638||0.96712||0.96784||0.96856||0.96926||0.96995||0.97062 |- ! 1.9 |0.97128||0.97193||0.97257||0.97320||0.97381||0.97441||0.97500||0.97558||0.97615||0.97670 |- | colspan="1" | |- ! 2.0 |0.97725||0.97778||0.97831||0.97882||0.97932||0.97982||0.98030||0.98077||0.98124||0.98169 |- ! 2.1 |0.98214||0.98257||0.98300||0.98341||0.98382||0.98422||0.98461||0.98500||0.98537||0.98574 |- ! 2.2 |0.98610||0.98645||0.98679||0.98713||0.98745||0.98778||0.98809||0.98840||0.98870||0.98899 |- ! 2.3 |0.98928||0.98956||0.98983||0.99010||0.99036||0.99061||0.99086||0.99111||0.99134||0.99158 |- ! 2.4 |0.99180||0.99202||0.99224||0.99245||0.99266||0.99286||0.99305||0.99324||0.99343||0.99361 |- | colspan="1" | |- ! 2.5 |0.99379||0.99396||0.99413||0.99430||0.99446||0.99461||0.99477||0.99492||0.99506||0.99520 |- ! 2.6 |0.99534||0.99547||0.99560||0.99573||0.99585||0.99598||0.99609||0.99621||0.99632||0.99643 |- ! 2.7 |0.99653||0.99664||0.99674||0.99683||0.99693||0.99702||0.99711||0.99720||0.99728||0.99736 |- ! 2.8 |0.99744||0.99752||0.99760||0.99767||0.99774||0.99781||0.99788||0.99795||0.99801||0.99807 |- ! 2.9 |0.99813||0.99819||0.99825||0.99831||0.99836||0.99841||0.99846||0.99851||0.99856||0.99861 |- | colspan="1" | |- ! 3.0 |0.99865||0.99869||0.99874||0.99878||0.99882||0.99886||0.99889||0.99893||0.99896||0.99900 |- ! 3.1 |0.99903||0.99906||0.99910||0.99913||0.99916||0.99918||0.99921||0.99924||0.99926||0.99929 |- ! 3.2 |0.99931||0.99934||0.99936||0.99938||0.99940||0.99942||0.99944||0.99946||0.99948||0.99950 |- ! 3.3 |0.99952||0.99953||0.99955||0.99957||0.99958||0.99960||0.99961||0.99962||0.99964||0.99965 |- ! 3.4 |0.99966||0.99968||0.99969||0.99970||0.99971||0.99972||0.99973||0.99974||0.99975||0.99976 |- | colspan="1" | |- ! 3.5 |0.99977||0.99978||0.99978||0.99979||0.99980||0.99981||0.99981||0.99982||0.99983||0.99983 |- ! 3.6 |0.99984||0.99985||0.99985||0.99986||0.99986||0.99987||0.99987||0.99988||0.99988||0.99989 |- ! 3.7 |0.99989||0.99990||0.99990||0.99990||0.99991||0.99991||0.99992||0.99992||0.99992||0.99992 |- ! 3.8 |0.99993||0.99993||0.99993||0.99994||0.99994||0.99994||0.99994||0.99995||0.99995||0.99995 |- ! 3.9 |0.99995||0.99995||0.99996||0.99996||0.99996||0.99996||0.99996||0.99996||0.99997||0.99997 |- | colspan="1" | |- ! 4.0 |0.99997||0.99997||0.99997||0.99997||0.99997||0.99997||0.99998||0.99998||0.99998||0.99998 |- ! *z* !! + 0.00!! + 0.01!! + 0.02!! + 0.03!! + 0.04!! + 0.05!! + 0.06!! + 0.07!! + 0.08!! + 0.09 |}
# 계산
{| class="wikitable sortable mw-collapsible mw-collapsed" |+ |- | align='center'| |- | (예시)z값 0.75 - 표준정규분포표 0.7의 행에서 +0.05의 열의 값 0.77337로부터 노란색 영역의 범위가 77.337%임를 쉽게 확인할 수 있다. |} {| class="wikitable" |- | align='center'| |- | (예시) z값 0 ~ 0.75 사이의 영역 값 |} : 0.75 (z값)- 표준정규분포표 0.7의 행에서 +0.05의 열의 값 0.77337을 확인할 수 있다. : 0 (z값)- 표준정규분포표 0의 행에서 +0.00의 열의 값 0.5를 확인할 수 있다. 따라서 z값 0 ~ 0.75 사이의 영역 값은 0.77337 - 0.5 = 0.27337 을 확인할 수 있다.