Em um banco, foi constatado após uma coleta de dados que o número médio de clientes que adquire um determinado seguro é de 6 por hora. Determine, e...

Para resolver esse problema, podemos utilizar a distribuição de Poisson. A fórmula para calcular a probabilidade de um determinado número de eventos ocorrer em um intervalo de tempo é dada por: P(X = k) = (e^-λ * λ^k) / k! Onde: - P(X = k) é a probabilidade de ocorrerem k eventos no intervalo de tempo; - e é a constante matemática aproximadamente igual a 2,71828; - λ é o número médio de eventos por unidade de tempo; - k é o número de eventos que queremos calcular a probabilidade; - k! é o fatorial de k. No caso do problema, temos que λ = 6, pois em média são vendidos 6 seguros por hora. Queremos calcular a probabilidade de serem vendidos exatamente 24 seguros em uma hora, ou seja, k = 24. Substituindo na fórmula, temos: P(X = 24) = (e^-6 * 6^24) / 24! Podemos simplificar a expressão, dividindo o numerador e o denominador por 24!, e obtemos: P(X = 24) = (e^-6 * 6^24) / (1 * 2 * 3 * ... * 23 * 24) Podemos calcular o valor de P(X = 24) utilizando uma calculadora científica ou uma tabela de distribuição de Poisson. O resultado é aproximadamente 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