L'intervalle de fluctuation

L'échantillonnage - Mathématiques BTS

Exercice 1 : Échantillonnage et intervalle de fluctuation

On étudie la fréquence d’un événement grâce au graphique ci-dessous représentant \( 100 \) échantillons.

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Déduire de ce graphique une valeur approchée de la taille \( N \) des échantillons puis choisir la valeur exacte la plus proche parmis les choix suivant.

\( N = \) 2500

\(N =\) 400

\( N = \) 280

\( N = \) 1100

\( N = \) 600

Exercice 2 : Intervalle de fluctuation pour une précision donnée (Formule Seconde)

Une entreprise X occupe 20% du marché.
Elle procède à un sondage sur 81 clients du marché en leur demandant s'ils sont clients de l'entreprise X.
En utilisant l'intervalle de fluctuation des fréquences à 95%, déterminer l'intervalle de clients qui devraient répondre positivement au sondage.

On donnera les bornes de l'intervalle sous la forme d'un entier.

Exercice 3 : Intervalle de fluctuation pour une précision donnée (Formule Seconde)

Soit un échantillon de \(361\) individus pris dans une population, on estime que la probabilité qu'un caractère soit présent chez un individu pris aléatoirement dans la population totale est de \(p = 0,24\).
Calculer l'intervalle de fluctuation des fréquences au seuil \(95\%\) de de la fréquence de ce caractère.
On arrondira les bornes à \(10^{-2}\) près. Par exemple, \([0,2386 ; 0,6394]\) deviendra \([0,24 ; 0,64]\).

Exercice 4 : Échantillonnage et intervalle de fluctuation

On étudie la fréquence d’un événement grâce au graphique ci-dessous représentant \( 100 \) échantillons.

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Déduire de ce graphique une valeur approchée de la taille \( N \) des échantillons puis choisir la valeur exacte la plus proche parmis les choix suivant.

\(N =\) 600

\( N = \) 400

\( N = \) 1100

\( N = \) 280

\( N = \) 2500

Exercice 5 : Intervalle de fluctuation pour une précision donnée (Formule Seconde)

Une entreprise X occupe 30% du marché.
Elle procède à un sondage sur 49 clients du marché en leur demandant s'ils sont clients de l'entreprise X.
En utilisant l'intervalle de fluctuation des fréquences à 95%, déterminer l'intervalle de clients qui devraient répondre positivement au sondage.

On donnera les bornes de l'intervalle sous la forme d'un entier.

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