{"id":6419,"date":"2025-07-15T13:34:48","date_gmt":"2025-07-15T13:34:48","guid":{"rendered":"https:\/\/functiontranslator.com\/loi-binomiale-inverse\/"},"modified":"2021-02-26T08:02:38","modified_gmt":"2021-02-26T08:02:38","slug":"binom-inv","status":"publish","type":"post","link":"https:\/\/functiontranslator.com\/fr\/binom-inv\/","title":{"rendered":"LOI.BINOMIALE.INVERSE"},"content":{"rendered":"

La fonction LOI.BINOMIALE.INVERSE de Microsoft Excel et son homologue BINOM.INV dans Google Sheets servent \u00e0 calculer le plus petit entier n pour lequel la somme des probabilit\u00e9s d’une distribution binomiale atteint ou d\u00e9passe une valeur sp\u00e9cifi\u00e9e. Cette fonction est couramment utilis\u00e9e dans les analyses statistiques qui concernent les distributions binomiales.<\/p>\n

Description de la fonction<\/h2>\n

La fonction LOI.BINOMIALE.INVERSE permet de d\u00e9terminer le nombre minimal de succ\u00e8s requis dans une s\u00e9rie d’essais pour qu’une probabilit\u00e9 de succ\u00e8s cumul\u00e9e sp\u00e9cifique soit atteinte. Elle est, par exemple, utilis\u00e9e pour estimer le seuil minimal de succ\u00e8s n\u00e9cessaire pour atteindre une probabilit\u00e9 cumul\u00e9e donn\u00e9e.<\/p>\n

Syntaxe :<\/p>\n

 LOI.BINOMIALE.INVERSE(n; probabilit\u00e9_succ\u00e8s; valeur_alpha)<\/code> <\/pre>\n
    \n
  • n<\/strong> : Le nombre total d\u2019essais.<\/li>\n
  • probabilit\u00e9_succ\u00e8s<\/strong> : La probabilit\u00e9 de succ\u00e8s pour un essai unique.<\/li>\n
  • valeur_alpha<\/strong> : La probabilit\u00e9 cumul\u00e9e cible.<\/li>\n<\/ul>\n
    Exemple d’utilisation :<\/p>\n
     =LOI.BINOMIALE.INVERSE(10; 0.5; 0.95)<\/code> <\/pre>\n
    Cette formule calcule le nombre minimal de succ\u00e8s n\u00e9cessaires parmi 10 essais pour que la probabilit\u00e9 cumul\u00e9e de succ\u00e8s atteigne au moins 95%, avec une probabilit\u00e9 de succ\u00e8s individuelle de 50%.<\/p>\n
    Application pratique 1: Planification de la qualit\u00e9 du produit<\/h2>\n
    Imaginons une entreprise qui produit des ampoules et veut garantir que dans un lot de 100 ampoules, la probabilit\u00e9 que moins de 95% d’entre elles soient fonctionnelles soit inf\u00e9rieure \u00e0 2%. Quel devrait \u00eatre le taux de succ\u00e8s minimal de chaque ampoule individuelle ?<\/p>\n
    Utilisation de la fonction :<\/p>\n
     =LOI.BINOMIALE.INVERSE(100; probabilit\u00e9_succ\u00e8s; 0.98)<\/code> <\/pre>\n
    En ajustant la \u00ab\u00a0probabilit\u00e9_succ\u00e8s\u00a0\u00bb jusqu’\u00e0 obtenir un r\u00e9sultat de 95 (ou le nombre le plus proche en dessous de 95), on peut d\u00e9terminer le pourcentage de r\u00e9ussite exig\u00e9.<\/p>\n
    Application pratique 2: Analyse de sc\u00e9nario en marketing<\/h2>\n
    Une campagne de marketing envisage d’envoyer 200 messages promotionnels \u00e0 des clients potentiels, avec l’objectif de convertir au moins 20% de ces contacts en achats. Quelle devrait \u00eatre la probabilit\u00e9 de succ\u00e8s par contact pour \u00eatre s\u00fbr \u00e0 90% d’atteindre cet objectif ?<\/p>\n
    Utilisation de la fonction :<\/p>\n
     =LOI.BINOMIALE.INVERSE(200; probabilit\u00e9_succ\u00e8s; 0.90)<\/code> <\/pre>\n
    Il faut ajuster le retour de la fonction pour garantir un r\u00e9sultat d’au moins 40 (soit 20% de 200). En modifiant ainsi la \u00ab\u00a0probabilit\u00e9_succ\u00e8s\u00a0\u00bb, on peut identifier la probabilit\u00e9 de succ\u00e8s n\u00e9cessaire par contact.<\/p>\n
    Ces exemples montrent comment la fonction LOI.BINOMIALE.INVERSE peut \u00eatre exploit\u00e9e pour prendre des d\u00e9cisions \u00e9clair\u00e9es dans divers contextes professionnels.<\/p>\n","protected":false},"excerpt":{"rendered":"
    Renvoie la plus petite valeuR pouR laquelle la distRibution binomiale cumul\u00e9e est inf\u00e9RieuRe ou \u00e9gale \u00e0 une valeuR de cRit\u00e8Re<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[315],"tags":[],"class_list":["post-6419","post","type-post","status-publish","format-standard","hentry","category-statistiques"],"acf":[],"yoast_head":"\nFonction BINOM.INV (LOI.BINOMIALE.INVERSE) dans Excel : comment \u00e7a marche, exemples et syntaxe<\/title>\n<meta name=\"description\" content=\"Pr\u00e9sentation de la fonction BINOM.INV (LOI.BINOMIALE.INVERSE) d\u2019Excel et Google Sheets. 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