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2- a) Considerando a situação podemos determinar os eleitores aleatórios como ???? de uma distribuição binomial, onde tomamos como sucesso os brasile...

2- a) Considerando a situação podemos determinar os eleitores aleatórios como ???? de uma distribuição binomial, onde tomamos como sucesso os brasileiros que votariam no candidato A. Portanto, sendo ???? o número de sucesso da amostra temos que ???? = 6 e com isso podemos mostrar a intenção de votos dos eleitores da seguinte forma: A partir desse gráfico entendemos que a probabilidade do candidato A obter sucesso nas eleições é de 6%, ou seja, ???? = 0,06. Assim, utilizando esse valor de ???? e analisando uma amostra maior ( 150 milhões de brasileiros), podemos obter um gráfico semelhante ao anterior, onde a esperança é ???? ???? = 9000000 e a variância é de ???? ???? = 8460000. b) Para uma amostra aleatória de 1000 eleitores com 60 votos para o candidato A e seguindo os procedimentos do item a, obtemos o seguinte gráfico: Podemos ver que este gráfico mostra-se mais preciso no valor 60, possuindo um desvio padrão menor. Contudo, analisando para os 150 milhões de brasileiros obtemos a mesma probabilidade, esperança e variância.
a) Calcular a probabilidade de X = 6
b) Analisar a intenção de votos dos eleitores com uma amostra de 150 milhões de brasileiros

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RA175182_ME414_L1
6 pág.

Estatística para Experimentalistas Universidade Federal do Espírito SantoUniversidade Federal do Espírito Santo

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a) Considerando que a situação apresentada se encaixa em uma distribuição binomial, onde o sucesso é a intenção de voto no candidato A, podemos determinar os eleitores aleatórios como tentativas independentes. Portanto, a probabilidade de X = 6 é dada por P(X = 6) = (n! / (x! * (n - x)!) * p^x * (1 - p)^(n - x)), onde n é o número de eleitores aleatórios, x é o número de sucessos, p é a probabilidade de sucesso e ! representa o fatorial. Substituindo os valores, temos P(X = 6) = (150000000! / (6! * (150000000 - 6)!) * 0,06^6 * (1 - 0,06)^(150000000 - 6)) ≈ 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