Determine as probabilidades de:
Passo 1
Primeiro, vamos entender o que a questão está pedindo. A questão quer que a gente determine a probabilidade de que a variável aleatória Z esteja entre -1,60 e 1,40. Estamos lidando com a distribuição normal padrão, que é uma distribuição de probabilidade contínua muito usada em estatística. Para resolver isso, vamos precisar usar a tabela da distribuição normal padrão ou uma calculadora que forneça valores de probabilidade para essa distribuição.
Passo 2
A distribuição normal padrão, representada por Z, tem média 0 e desvio padrão 1. A probabilidade que queremos calcular,
, significa a área sob a curva normal entre Z = -1,60 e Z = 1,40.
Passo 3
Para encontrar essa probabilidade, vamos calcular duas probabilidades separadas:
-
: a probabilidade de Z ser menor que 1,40. -
: a probabilidade de Z ser menor que -1,60.
Passo 4
Usando a tabela da distribuição normal padrão ou uma calculadora:
-
≈ 0,9192 -
≈ 0,0548
Passo 5
Agora, para encontrar a probabilidade entre -1,60 e 1,40, subtraímos a segunda probabilidade da primeira:
Resposta
A probabilidade de que Z esteja entre -1,60 e 1,40 é aproximadamente 0,8644 ou 86,44%.
Exercícios relacionados
Calcule, caso existam, os seguintes linites:
Utilize o teste dos caminhos para provar a não existencia dos seguintes limites:
<html><head></head><body><div>Determine as probabilidades de: <span class="math-inline ">
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<html><head></head><body><div>Determine as probabilidades de: <span class="math-inline ">
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