{"id":1044,"date":"2023-07-27T20:56:00","date_gmt":"2023-07-27T20:56:00","guid":{"rendered":"https:\/\/statorials.org\/pl\/obszar-pokazany-pod-standardowa-krzywa-normalna\/"},"modified":"2023-07-27T20:56:00","modified_gmt":"2023-07-27T20:56:00","slug":"obszar-pokazany-pod-standardowa-krzywa-normalna","status":"publish","type":"post","link":"https:\/\/statorials.org\/pl\/obszar-pokazany-pod-standardowa-krzywa-normalna\/","title":{"rendered":"Jak znale\u017a\u0107 wskazany obszar pod standardow\u0105 krzyw\u0105 normaln\u0105"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">Jednym z najcz\u0119stszych pyta\u0144 w statystyce elementarnej jest:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u201eZnajd\u017a wskazany obszar pod standardow\u0105 krzyw\u0105 normaln\u0105.\u201d<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Mo\u017cna odpowiedzie\u0107 na tego typu pytania korzystaj\u0105c z warto\u015bci znajduj\u0105cych si\u0119 w tabeli z. W tym samouczku wyja\u015bniono, jak u\u017cywa\u0107 tabeli z do odpowiadania na nast\u0119puj\u0105ce cztery typy pyta\u0144:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Znajd\u017a obszar pod krzyw\u0105 poni\u017cej pewnej warto\u015bci.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Znajd\u017a pole pod krzyw\u0105 wi\u0119ksze od okre\u015blonej warto\u015bci.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Znajd\u017a pole pod krzyw\u0105 pomi\u0119dzy dwiema warto\u015bciami.<\/span><\/li>\n<li> <span style=\"color: #000000;\">Znajd\u017a pole pod krzyw\u0105 poza dwiema warto\u015bciami.<\/span><\/li>\n<\/ul>\n<h3> <span style=\"color: #000000;\"><strong>Przyk\u0142ad 1: Znajd\u017a wskazany obszar mniejszy od okre\u015blonej warto\u015bci<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\"><strong>Pytanie:<\/strong> Znajd\u017a pole pod standardow\u0105 krzyw\u0105 normaln\u0105 na lewo od z = 1,26.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Rozwi\u0105zanie:<\/strong> Aby odpowiedzie\u0107 na to pytanie, po prostu przeszukaj tabel\u0119 z pod k\u0105tem warto\u015bci odpowiadaj\u0105cej 1,26:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-10809 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/indique1.png\" alt=\"Znajd\u017a wskazany obszar pod standardow\u0105 krzyw\u0105 normaln\u0105\" width=\"612\" height=\"414\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Pole pod standardow\u0105 krzyw\u0105 normaln\u0105 na lewo od z = 1,26 wynosi <strong>0,8962<\/strong> .<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Przyk\u0142ad 2: Znajd\u017a wskazany obszar wi\u0119kszy od okre\u015blonej warto\u015bci<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\"><strong>Pytanie:<\/strong> Znajd\u017a pole pod standardow\u0105 krzyw\u0105 normaln\u0105 na prawo od z = -1,81.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Rozwi\u0105zanie:<\/strong> Aby odpowiedzie\u0107 na to pytanie, po prostu przeszukaj tabel\u0119 z pod k\u0105tem warto\u015bci odpowiadaj\u0105cej -1,81 i odejmij j\u0105 od 1:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-10810 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/indique2.png\" alt=\"\" width=\"599\" height=\"387\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Pole pod standardow\u0105 krzyw\u0105 normaln\u0105 na prawo od z = -1,81 wynosi 1 \u2013 0,0351 \u2013 <strong>0,9649<\/strong> .<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Przyk\u0142ad 3: Znajd\u017a okre\u015blony obszar pomi\u0119dzy dwiema warto\u015bciami<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\"><strong>Pytanie:<\/strong> Znajd\u017a pole pod standardow\u0105 krzyw\u0105 normaln\u0105 pomi\u0119dzy z = -1,81 a z = 1,26<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Rozwi\u0105zanie:<\/strong> Aby odpowiedzie\u0107 na to pytanie, wystarczy odj\u0105\u0107 pole na lewo od z = -1,81 od pola na lewo od 1,26.<\/span><\/p>\n<p> <span style=\"color: #000000;\">W poprzednich przyk\u0142adach odkryli\u015bmy, \u017ce obszar na lewo od z = -1,81 wynosi\u0142 0,0351, a obszar na lewo od z = 1,26 wynosi\u0142 0,8962.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Zatem pole pod standardow\u0105 krzyw\u0105 normaln\u0105 pomi\u0119dzy z = -1,81 a z = 1,26 wynosi 0,8962 \u2013 0,0351 = <strong>0,8611<\/strong> .<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Przyk\u0142ad 4: Znajd\u017a okre\u015blony obszar poza dwiema warto\u015bciami<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\"><strong>Pytanie:<\/strong> Znajd\u017a pole pod standardow\u0105 krzyw\u0105 normaln\u0105 poza z = -1,81 i z = 1,26<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Rozwi\u0105zanie:<\/strong> Aby odpowiedzie\u0107 na to pytanie, musimy doda\u0107 pole po lewej stronie z = -1,81 i pole po prawej stronie z = 1,26.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Pole na lewo od z = -1,81 wynosi <strong>0,0351<\/strong> , a pole na prawo od z = 1,26 wynosi 1-0,8962 = <strong>0,1038<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Zatem obszar pomi\u0119dzy z = -1,81 i z = 1,26 wynosi 0,0351 + 0,1038 = <strong>0,1389<\/strong> .<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Bonus: standardowy kalkulator powierzchni krzywej normalnej<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Mo\u017cesz u\u017cy\u0107 <a href=\"https:\/\/statorials.org\/pl\/szybki-normalny-kalkulator-cdf\/\" target=\"_blank\" rel=\"noopener noreferrer\">tego kalkulatora<\/a> , aby automatycznie znale\u017a\u0107 pole pod standardow\u0105 krzyw\u0105 normaln\u0105 pomi\u0119dzy dwiema warto\u015bciami.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Jednym z najcz\u0119stszych pyta\u0144 w statystyce elementarnej jest: \u201eZnajd\u017a wskazany obszar pod standardow\u0105 krzyw\u0105 normaln\u0105.\u201d Mo\u017cna odpowiedzie\u0107 na tego typu pytania korzystaj\u0105c z warto\u015bci znajduj\u0105cych si\u0119 w tabeli z. W tym samouczku wyja\u015bniono, jak u\u017cywa\u0107 tabeli z do odpowiadania na nast\u0119puj\u0105ce cztery typy pyta\u0144: Znajd\u017a obszar pod krzyw\u0105 poni\u017cej pewnej warto\u015bci. Znajd\u017a pole pod krzyw\u0105 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-1044","post","type-post","status-publish","format-standard","hentry","category-przewodnik"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Jak znale\u017a\u0107 wskazany obszar pod standardow\u0105 krzyw\u0105 normaln\u0105<\/title>\n<meta name=\"description\" content=\"Proste wyja\u015bnienie, jak znale\u017a\u0107 obszary pokazane pod standardow\u0105 krzyw\u0105 normaln\u0105.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/pl\/obszar-pokazany-pod-standardowa-krzywa-normalna\/\" \/>\n<meta property=\"og:locale\" content=\"pl_PL\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Jak znale\u017a\u0107 wskazany obszar pod standardow\u0105 krzyw\u0105 normaln\u0105\" \/>\n<meta property=\"og:description\" content=\"Proste wyja\u015bnienie, jak znale\u017a\u0107 obszary pokazane pod standardow\u0105 krzyw\u0105 normaln\u0105.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pl\/obszar-pokazany-pod-standardowa-krzywa-normalna\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-27T20:56:00+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/indique1.png\" \/>\n<meta name=\"author\" content=\"Benjamin Anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Napisane przez\" \/>\n\t<meta name=\"twitter:data1\" content=\"Benjamin Anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Szacowany czas czytania\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minuty\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/pl\/obszar-pokazany-pod-standardowa-krzywa-normalna\/\",\"url\":\"https:\/\/statorials.org\/pl\/obszar-pokazany-pod-standardowa-krzywa-normalna\/\",\"name\":\"Jak znale\u017a\u0107 wskazany obszar pod standardow\u0105 krzyw\u0105 normaln\u0105\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pl\/#website\"},\"datePublished\":\"2023-07-27T20:56:00+00:00\",\"dateModified\":\"2023-07-27T20:56:00+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pl\/#\/schema\/person\/6484727a4612df3e69f016c3129c6965\"},\"description\":\"Proste wyja\u015bnienie, jak znale\u017a\u0107 obszary pokazane pod standardow\u0105 krzyw\u0105 normaln\u0105.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pl\/obszar-pokazany-pod-standardowa-krzywa-normalna\/#breadcrumb\"},\"inLanguage\":\"pl-PL\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pl\/obszar-pokazany-pod-standardowa-krzywa-normalna\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pl\/obszar-pokazany-pod-standardowa-krzywa-normalna\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Dom\",\"item\":\"https:\/\/statorials.org\/pl\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Jak znale\u017a\u0107 wskazany obszar pod standardow\u0105 krzyw\u0105 normaln\u0105\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/pl\/#website\",\"url\":\"https:\/\/statorials.org\/pl\/\",\"name\":\"Statorials\",\"description\":\"Tw\u00f3j przewodnik po kompetencjach statystycznych!\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/pl\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"pl-PL\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/pl\/#\/schema\/person\/6484727a4612df3e69f016c3129c6965\",\"name\":\"Benjamin Anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"pl-PL\",\"@id\":\"https:\/\/statorials.org\/pl\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/statorials.org\/pl\/wp-content\/uploads\/2023\/11\/Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"https:\/\/statorials.org\/pl\/wp-content\/uploads\/2023\/11\/Benjamin-Anderson-96x96.jpg\",\"caption\":\"Benjamin Anderson\"},\"description\":\"Cze\u015b\u0107, jestem Benjamin i jestem emerytowanym profesorem statystyki, kt\u00f3ry zosta\u0142 oddanym nauczycielem Statorials. 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