{"id":232,"date":"2023-08-03T20:48:38","date_gmt":"2023-08-03T20:48:38","guid":{"rendered":"https:\/\/statorials.org\/pt\/distribuicao-binomial-1\/"},"modified":"2023-08-03T20:48:38","modified_gmt":"2023-08-03T20:48:38","slug":"distribuicao-binomial-1","status":"publish","type":"post","link":"https:\/\/statorials.org\/pt\/distribuicao-binomial-1\/","title":{"rendered":"Distribui\u00e7\u00e3o binomial"},"content":{"rendered":"<p>Este artigo explica o que \u00e9 a distribui\u00e7\u00e3o binomial nas estat\u00edsticas e para que ela \u00e9 usada. Voc\u00ea encontrar\u00e1, portanto, a defini\u00e7\u00e3o da distribui\u00e7\u00e3o binomial, exemplos de distribui\u00e7\u00f5es binomiais e as propriedades deste tipo de distribui\u00e7\u00e3o de probabilidade. Al\u00e9m disso, voc\u00ea poder\u00e1 calcular qualquer probabilidade da distribui\u00e7\u00e3o binomial com uma calculadora online. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-es-la-distribucion-binomial\"><\/span> Qual \u00e9 a distribui\u00e7\u00e3o binomial?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A <strong>distribui\u00e7\u00e3o binomial<\/strong> \u00e9 uma distribui\u00e7\u00e3o de probabilidade que conta o n\u00famero de sucessos ao realizar uma s\u00e9rie de experimentos independentes e dicot\u00f4micos com uma probabilidade de sucesso constante.<\/p>\n<p> Em outras palavras, a distribui\u00e7\u00e3o binomial \u00e9 uma distribui\u00e7\u00e3o que descreve o n\u00famero de resultados bem-sucedidos de uma sequ\u00eancia de tentativas de Bernoulli.<\/p>\n<p> Lembre-se de que um teste de Bernoulli \u00e9 um experimento que tem dois resultados poss\u00edveis: \u201csucesso\u201d e \u201cfracasso\u201d. Portanto, se a probabilidade de \u201csucesso\u201d for <em>p<\/em> , a probabilidade de \u201cfracasso\u201d \u00e9 <em>q=1-p<\/em> .<\/p>\n<p> Em geral, o n\u00famero total de experimentos realizados \u00e9 definido com o par\u00e2metro <em>n<\/em> , enquanto <em>p<\/em> \u00e9 a probabilidade de sucesso de cada experimento. Assim, uma vari\u00e1vel aleat\u00f3ria que segue uma distribui\u00e7\u00e3o binomial \u00e9 escrita da seguinte forma:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-2f2b2be5bfe6c63bd13c552f4c893f59_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\sim\\text{Bin}(n,p)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"107\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Observe que em uma distribui\u00e7\u00e3o binomial, exatamente o mesmo experimento \u00e9 repetido <em>n<\/em> vezes e os experimentos s\u00e3o independentes um do outro, portanto a probabilidade de sucesso de cada experimento \u00e9 a mesma <em>(p)<\/em> .<\/p>\n<p> A distribui\u00e7\u00e3o binomial tamb\u00e9m pode ser chamada de <strong>distribui\u00e7\u00e3o binomial<\/strong> . <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplos-de-la-distribucion-binomial\"><\/span> Exemplos de distribui\u00e7\u00e3o binomial<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Depois de vermos a defini\u00e7\u00e3o da distribui\u00e7\u00e3o binomial, veremos v\u00e1rios exemplos de vari\u00e1veis que seguem este tipo de distribui\u00e7\u00e3o para melhor compreender o conceito.<\/p>\n<ol style=\"color:#FF8A05; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">N\u00famero de vezes que aparece cara ao lan\u00e7ar uma moeda 25 vezes.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">N\u00famero de arremessos dados por um jogador de basquete ao arremessar 60 vezes em dire\u00e7\u00e3o \u00e0 cesta do mesmo local.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">N\u00famero de vezes que obtemos o n\u00famero 6 lan\u00e7ando um dado 30 vezes.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">N\u00famero de aprova\u00e7\u00f5es de um total de 50 alunos fazendo um exame.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\">N\u00famero de unidades defeituosas em uma amostra de 100 produtos.<\/span> <\/li>\n<\/ol>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-la-distribucion-binomial\"><\/span> F\u00f3rmula de distribui\u00e7\u00e3o binomial<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Dados os par\u00e2metros <em>x, n, p,<\/em> a fun\u00e7\u00e3o de probabilidade da distribui\u00e7\u00e3o binomial \u00e9 definida como o n\u00famero combinat\u00f3rio de <em>n<\/em> em <em>x<\/em> vezes <em>p <sup>x<\/sup><\/em> vezes <em>(1-p) <sup>nx<\/sup><\/em> .<\/p>\n<p> Portanto, a <strong>f\u00f3rmula para calcular a probabilidade de uma distribui\u00e7\u00e3o binomial<\/strong> \u00e9: <\/p>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/distribution-binomiale.png\" alt=\"F\u00f3rmula de distribui\u00e7\u00e3o binomial\" class=\"wp-image-4636\" width=\"291\" height=\"290\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> \ud83d\udc49 <u style=\"text-decoration-color:#FF8A05;\">Voc\u00ea pode usar a calculadora abaixo para calcular a probabilidade de uma vari\u00e1vel que segue a distribui\u00e7\u00e3o binomial.<\/u><\/p>\n<p> Por outro lado, a probabilidade cumulativa da distribui\u00e7\u00e3o binomial \u00e9 calculada somando as probabilidades do n\u00famero de casos de sucesso em quest\u00e3o e todas as probabilidades anteriores. Portanto, a f\u00f3rmula para calcular uma probabilidade cumulativa de uma distribui\u00e7\u00e3o binomial \u00e9: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-e31ef4ae023b8bf51c0b6816bc787c91_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[X\\leq x]=\\sum_{k=0}^x\\begin{pmatrix}n\\\\k\\end{pmatrix}p^k(1-p)^{n-k}\" title=\"Rendered by QuickLaTeX.com\" height=\"50\" width=\"262\" style=\"vertical-align: -22px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicio-resuelto-de-la-distribucion-binomial\"><\/span> Exerc\u00edcio resolvido sobre distribui\u00e7\u00e3o binomial<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li> Lan\u00e7amos uma moeda 10 vezes, qual \u00e9 a probabilidade de obter 6 caras?<\/li>\n<\/ul>\n<p> A vari\u00e1vel neste problema segue uma distribui\u00e7\u00e3o binomial porque todos os lan\u00e7amentos s\u00e3o independentes entre si e tamb\u00e9m t\u00eam a mesma probabilidade de sucesso.<\/p>\n<p> Concretamente, a probabilidade de sucesso \u00e9 de 50%, uma vez que apenas um dos dois resultados poss\u00edveis \u00e9 considerado um sucesso.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-bdceac6409b69d142f23801ec85e2691_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p=\\cfrac{1}{2}=0,5\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"93\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Portanto, a distribui\u00e7\u00e3o para este exerc\u00edcio \u00e9 um bin\u00f4mio com um total de 10 experimentos e uma probabilidade de 0,5.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-b460c8983298ba0cf52c05f460905732_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\sim\\text{Bin}(10 ; 0,5)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"131\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Portanto, para determinar a probabilidade de obter seis caras, precisamos aplicar a f\u00f3rmula de distribui\u00e7\u00e3o binomial.<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-17346d59c641378880b734dfe88210f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}P[X=x]&amp;=\\begin{pmatrix}n\\\\x\\end{pmatrix}p^x(1-p)^{n-x}\\\\[2ex]P[X=6]&amp;=\\begin{pmatrix}10\\\\6\\end{pmatrix}0,5^6(1-0,5)^{10-6}\\\\[2ex]P[X=6]&amp;=0,2051\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"151\" width=\"279\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Portanto, a probabilidade de obter exatamente seis caras jogando uma moeda dez vezes \u00e9 de 20,51%. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"caracteristicas-de-la-distribucion-binomial\"><\/span> Caracter\u00edsticas da distribui\u00e7\u00e3o binomial<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A distribui\u00e7\u00e3o binomial possui as seguintes caracter\u00edsticas:<\/p>\n<ul>\n<li> A distribui\u00e7\u00e3o binomial \u00e9 definida com dois par\u00e2metros: <em>n<\/em> \u00e9 o n\u00famero total de experimentos de Bernoulli e, por outro lado, <em>p<\/em> \u00e9 a probabilidade de sucesso de cada experimento de Bernoulli.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-cd9728a237a5f49107bf14f440620936_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}X\\sim\\text{Bin}(n,p)\\\\[2ex]n\\geq 0\\\\[2ex]0\\leq p\\leq 1\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"93\" width=\"108\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> A m\u00e9dia de uma distribui\u00e7\u00e3o binomial \u00e9 igual ao produto do n\u00famero total de experimentos multiplicado pela probabilidade de sucesso de cada experimento. Portanto, para calcular a m\u00e9dia de uma distribui\u00e7\u00e3o binomial, deve-se multiplicar <em>n<\/em> por <em>p<\/em> .<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-65db1683dc8790001072c564aadf3631_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"E[X]=n\\cdot p\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"96\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> A vari\u00e2ncia de uma distribui\u00e7\u00e3o binomial \u00e9 igual ao n\u00famero total de tentativas multiplicado pela probabilidade de sucesso e pela probabilidade de fracasso.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-103608d604d211c1bd995dd3f982d11b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Var(X)=n\\cdot p\\cdot (1-p)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"183\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> A f\u00f3rmula para a fun\u00e7\u00e3o de probabilidade da distribui\u00e7\u00e3o binomial \u00e9 a seguinte:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-3ab3244961c8b68181859f8a87b2811c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[X=x]&amp;=\\begin{pmatrix}n\\\\ x\\end{pmatrix}p^x(1-p)^{n-x}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"235\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<ul>\n<li> Da mesma forma, a f\u00f3rmula para a fun\u00e7\u00e3o de distribui\u00e7\u00e3o cumulativa da distribui\u00e7\u00e3o binomial \u00e9:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-e31ef4ae023b8bf51c0b6816bc787c91_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[X\\leq x]=\\sum_{k=0}^x\\begin{pmatrix}n\\\\k\\end{pmatrix}p^k(1-p)^{n-k}\" title=\"Rendered by QuickLaTeX.com\" height=\"50\" width=\"262\" style=\"vertical-align: -22px;\"><\/p>\n<\/p>\n<ul>\n<li> A soma de duas distribui\u00e7\u00f5es binomiais independentes com a mesma probabilidade \u00e9 equivalente a uma distribui\u00e7\u00e3o binomial com o mesmo valor de probabilidade <em>p<\/em> e sendo <em>n<\/em> a soma do n\u00famero total de tentativas das duas distribui\u00e7\u00f5es.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-dbc1a01b2d5654864d688cc46ac3a2e6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c}X\\sim\\text{Bin}(n,p)\\qquad Y\\sim\\text{Bin}(m,p)\\\\[4ex]Z=X+Y \\sim\\text{Bin}(n+m,p)\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"72\" width=\"254\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-9fed580dc5cfbce19048124974a1fa41_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle P[Z=z]=\\begin{pmatrix}n+m\\\\z\\end{pmatrix}p^z(1-p)^{n+m-z}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"289\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<ul>\n<li> A distribui\u00e7\u00e3o de Bernoulli \u00e9 um caso especial de distribui\u00e7\u00e3o binomial em que <em>n=1<\/em> , ou seja, apenas um experimento \u00e9 realizado.<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-919200bea19252a9f6bee424ad48908d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\sim\\text{Bin}(1,p) \\quad \\color{orange}\\bm{\\longrightarrow}\\color{black}\\quad X\\sim\\text{Bernoulli}(p)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"397\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> <em><sub>Se<\/sub> <sub>X<\/sub><\/em> 1 <em>,<\/em> <em><sub>X<\/sub> <sub>2<\/sub> ,\u2026, X <sub>k<\/sub><\/em> s\u00e3o vari\u00e1veis aleat\u00f3rias independentes tais que <\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-1bc264e1007f09c3701e65ae678115b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\sum_{i=1}^k X_i\\sim \\text{Bin}\\left(\\sum_{i=1}^k n_i,p\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"188\" style=\"vertical-align: -23px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"calculadora-de-la-distribucion-binomial\"><\/span> Calculadora de distribui\u00e7\u00e3o binomial<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Insira os valores dos par\u00e2metros <em>p, n<\/em> e <em>x<\/em> da distribui\u00e7\u00e3o binomial na calculadora a seguir para calcular a probabilidade. Voc\u00ea precisa selecionar a probabilidade que deseja calcular e inserir os n\u00fameros usando o ponto como separador decimal, por exemplo 0,1667.<\/p>\n<form action=\"\" method=\"post\">\n<div style=\"margin-bottom:20px; margin-left:5%\"> <span style=\"color:#101010;font-weight: normal;\"><span style=\"color:#1C2C92\"><strong>\u27a4<\/strong><\/span> Probabilidade de sucesso de cada experimento <span style=\"color:#1C2C92\"><strong>\u2192<\/strong><\/span><\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-e67f693705a2e492d8981f0ed1387c3f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p = \" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"28\" style=\"vertical-align: -4px;\"><\/p>\n<p><\/span> <input name=\"prob\" style=\"border:1.5px solid #4FC3F7; border-radius:5px;  padding:7px; color:#000000; background-color:#EBF5FB; width:60px\" required=\"\" oninvalid=\"this.setCustomValidity('Introduce la probabilidad de \u00e9xito de cada experimento aqu\u00ed')\" oninput=\"this.setCustomValidity('')\"><\/div>\n<div style=\"margin-bottom:20px; margin-left:5%\"> <span style=\"color:#101010;font-weight: normal;\"><span style=\"color:#1C2C92\"><strong>\u27a4<\/strong><\/span> N\u00famero total de experimentos realizados <span style=\"color:#1C2C92\"><strong>\u2192<\/strong><\/span><\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-17b8c0c4e843e448cbe5846755391d66_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n = \" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"29\" style=\"vertical-align: 0px;\"><\/p>\n<p><\/span> <input name=\"n\" style=\"border:1.5px solid #4FC3F7; border-radius:5px;  padding:7px; color:#000000; background-color:#EBF5FB; width:60px\" required=\"\" oninvalid=\"this.setCustomValidity('Introduce el n\u00famero total de experimentos realizados aqu\u00ed')\" oninput=\"this.setCustomValidity('')\"><\/div>\n<div style=\"margin-bottom:14px; margin-left:5%\"> <span style=\"color:#1C2C92\"><strong>\u27a4<\/strong><\/span> N\u00famero de experimentos bem-sucedidos: <\/div>\n<div style=\"margin-bottom:14px; margin-left:10%\"><input name=\"tipoprobabilidad\" type=\"radio\" checked=\"\" value=\"probigual\"><\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-95a78799e4906daa08ea620a942c61bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X=\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"34\" style=\"vertical-align: 0px;\"><\/p>\n<p><input name=\"xigual\" style=\"border:1.5px solid #4FC3F7; border-radius:5px;  padding:7px; color:#000000; background-color:#EBF5FB; width:60px\"><\/div>\n<div style=\"margin-bottom:14px; margin-left:10%\"><input name=\"tipoprobabilidad\" type=\"radio\" value=\"probcolaizquierda\"><\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-305e8313d9decdf3d650c7f6898a8430_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\leq\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"34\" style=\"vertical-align: -3px;\"><\/p>\n<p><input name=\"xmenor\" style=\"border:1.5px solid #4FC3F7; border-radius:5px;  padding:7px; color:#000000; background-color:#EBF5FB; width:60px\"><\/div>\n<div style=\"margin-bottom:14px; margin-left:10%\"><input name=\"tipoprobabilidad\" type=\"radio\" value=\"probcoladerecha\"><\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-a8500b9856a735bc31ea1a371fc0fe88_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"X\\geq\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"34\" style=\"vertical-align: -3px;\"><\/p>\n<p><input name=\"xmayor\" style=\"border:1.5px solid #4FC3F7; border-radius:5px;  padding:7px; color:#000000; background-color:#EBF5FB; width:60px\"><\/div>\n<div style=\"margin-bottom:14px; margin-left:10%\"><input name=\"tipoprobabilidad\" type=\"radio\" value=\"probentre\"><input name=\"xentre1\" style=\"border:1.5px solid #4FC3F7; border-radius:5px;  padding:7px; color:#000000; background-color:#EBF5FB; width:60px\"><\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-a4459b2c5c9a9dd4efd3c3c155cb80bc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\leq X\\leq \" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"52\" style=\"vertical-align: -3px;\"><\/p>\n<p><input name=\"xentre2\" style=\"border:1.5px solid #4FC3F7; border-radius:5px;  padding:7px; color:#000000; background-color:#EBF5FB; width:60px\"><\/div>\n<div style=\"text-align:center\"><input align=\"center\" style=\"border-radius:30px; margin: 20px\" type=\"submit\" name=\"submit\" value=\"Calcule a probabilidade\"><\/div>\n<\/form>\n","protected":false},"excerpt":{"rendered":"<p>Este artigo explica o que \u00e9 a distribui\u00e7\u00e3o binomial nas estat\u00edsticas e para que ela \u00e9 usada. Voc\u00ea encontrar\u00e1, portanto, a defini\u00e7\u00e3o da distribui\u00e7\u00e3o binomial, exemplos de distribui\u00e7\u00f5es binomiais e as propriedades deste tipo de distribui\u00e7\u00e3o de probabilidade. Al\u00e9m disso, voc\u00ea poder\u00e1 calcular qualquer probabilidade da distribui\u00e7\u00e3o binomial com uma calculadora online. 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