Après réalisation d'une enquête, on estime que le temps en minutes, consacré
quotidiennement par un élève à faire ses devoirs scolaires, est une variable
aléatoire \(X\) suivant une loi normale d'espérance 65 minutes et d'écart-type
11 minutes.
L'allure de la courbe de densité de cette loi normale est représentée ci-dessous.
L'égalité \(P\left(X \le 49 \right) = 0,073 \) est illustrée graphiquement.
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Dans tout l'exercice, on donnera des réponses à \(10^{-3}\) près.
Déterminer la probabilité qu'un élève consacre quotidiennement moins de 65 minutes à faire ses devoirs scolaires.