Quiz — 662d1846d8488_Enoncé-statestique.pdf

Question 1 sur 10 20:00

[{"id":25024,"question":"Quelle est la probabilité d'obtenir exactement 3 fois pile en 5 lancers d'une pièce équilibrée ?","option_a":"A. 5\/16","option_b":"B. 10\/32","option_c":"C. 3\/8","option_d":"D. 1\/4","option_e":"","option_f":"","bonne_reponse":"b","explication":"La loi binomiale donne P(X=3) = C(5,3) * (1\/2)^5 = 10\/32. C'est une application directe de la formule des probabilités binomiales.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"A. 5\/16\", \"b\": \"B. 10\/32\", \"c\": \"C. 3\/8\", \"d\": \"D. 1\/4\"}}","_debug_options_count":4},{"id":25025,"question":"Dans une série statistique, si l'écart-type est nul, alors :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Un écart-type nul signifie que toutes les valeurs sont identiques, donc la série est constante.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":25026,"question":"La régression linéaire permet de :","option_a":"A. Calculer la moyenne d'une série","option_b":"B. Trouver la droite qui minimise l'erreur quadratique","option_c":"C. Déterminer la variance d'une variable aléatoire","option_d":"D. Calculer une probabilité conditionnelle","option_e":"","option_f":"","bonne_reponse":"b","explication":"La régression linéaire vise à ajuster une droite aux données pour modéliser leur relation linéaire.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"A. Calculer la moyenne d'une série\", \"b\": \"B. Trouver la droite ","_debug_options_count":4},{"id":25027,"question":"Si X suit une loi normale N(0,1), alors P(X ≤ -1,96) est égale à :","option_a":"A. 0,025","option_b":"B. 0,975","option_c":"C. 0,5","option_d":"D. 0,05","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour une loi normale centrée réduite, P(X ≤ -1,96) ≈ 0,025 (valeur tabulée).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A. 0,025\", \"b\": \"B. 0,975\", \"c\": \"C. 0,5\", \"d\": \"D. 0,05\"}}","_debug_options_count":4},{"id":25028,"question":"Le coefficient de corrélation linéaire r entre deux variables X et Y vérifie toujours :","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le coefficient r est toujours compris entre -1 et 1, mais il peut être égal à 0 (pas de corrélation linéaire).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":25029,"question":"Quelle formule donne la variance d'une série statistique ?","option_a":"A. σ² = Σ(xi - μ)² \/ n","option_b":"B. σ² = Σxi² \/ n - μ²","option_c":"C. σ² = (Σxi)² \/ n - μ","option_d":"D. σ² = Σ(xi - μ) \/ n","option_e":"","option_f":"","bonne_reponse":"a","explication":"La variance est la moyenne des carrés des écarts à la moyenne : σ² = Σ(xi - μ)² \/ n.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A. σ² = Σ(xi - μ)² \/ n\", \"b\": \"B. σ² = Σxi² \/ n - μ²\",","_debug_options_count":4},{"id":25030,"question":"Dans une loi binomiale B(n,p), l'espérance est égale à :","option_a":"A. n*p","option_b":"B. n*(1-p)","option_c":"C. p*(1-p)","option_d":"D. n*p*(1-p)","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'espérance d'une loi binomiale B(n,p) est E(X) = n*p, où n est le nombre d'essais et p la probabilité de succès.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A. n*p\", \"b\": \"B. n*(1-p)\", \"c\": \"C. p*(1-p)\", \"d\": \"D. n*p*(1-p)","_debug_options_count":4},{"id":25031,"question":"Si deux événements A et B sont indépendants, alors P(A ∩ B) = P(A) * P(B).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est la définition de l'indépendance entre deux événements : P(A ∩ B) = P(A) * P(B).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":25032,"question":"Quelle est la valeur de l'écart-type d'une série {2, 2, 2, 2} ?","option_a":"A. 0","option_b":"B. 2","option_c":"C. 4","option_d":"D. 1","option_e":"","option_f":"","bonne_reponse":"a","explication":"Toutes les valeurs étant identiques, l'écart-type est nul (pas de dispersion).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A. 0\", \"b\": \"B. 2\", \"c\": \"C. 4\", \"d\": \"D. 1\"}}","_debug_options_count":4},{"id":25033,"question":"La droite de régression passe toujours par le point (μx, μy), où μx et μy sont les moyennes des variables X et Y.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est une propriété fondamentale de la régression linéaire : la droite passe par le centre de gravité des données.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4}]