Question
perform the following complete probability exercise on a calculator Banco del País recently started a new credit program. Customers who meet certain credit requirements can obtain a credit card that is accepted by area merchants. Previous records indicate that 25% of all applicants for this type of card are rejected. If a total of 5 applications are received in one day, what is the probability that exactly 3 will be rejected? Select one: to The probability that exactly 3 are rejected is 98.44% b. The probability that exactly 3 are rejected is 10.35% c. The probability that exactly 3 are rejected is 0.09% d. The probability that exactly 3 are rejected is 8.79%
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Answer to a math question perform the following complete probability exercise on a calculator Banco del País recently started a new credit program. Customers who meet certain credit requirements can obtain a credit card that is accepted by area merchants. Previous records indicate that 25% of all applicants for this type of card are rejected. If a total of 5 applications are received in one day, what is the probability that exactly 3 will be rejected? Select one: to The probability that exactly 3 are rejected is 98.44% b. The probability that exactly 3 are rejected is 10.35% c. The probability that exactly 3 are rejected is 0.09% d. The probability that exactly 3 are rejected is 8.79%
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4.8113 Answers
La probabilidad de que una solicitud sea rechazada es del 25%, por lo tanto, la probabilidad de que una solicitud sea aceptada es del 75%.
Usaremos la distribución binomial para calcular la probabilidad de que exactamente 3 de las 5 solicitudes sean rechazadas.
La fórmula para la distribución binomial es:
P(X = k) = \binom{n}{k} \cdot p^k \cdot (1-p)^{n-k}
Donde:
-n = 5
-k = 3
-p = 0.25
-1-p = 0.75
Sustituyendo estos valores en la fórmula:
P(X = 3) = \binom{5}{3} \cdot (0.25)^3 \cdot (0.75)^{2}
Calculamos\binom{5}{3} = \frac{5!}{3!(5-3)!} = \frac{5 \cdot 4}{2 \cdot 1} = 10
Entonces,
P(X = 3) = 10 \cdot (0.25)^3 \cdot (0.75)^2 = 10 \cdot 0.015625 \cdot 0.5625 = 0.08789
Por lo tanto, la probabilidad de que exactamente 3 de las 5 solicitudes sean rechazadas es del 8.79%.
\boxed{\text{La probabilidad de que exactamente 3 sean rechazadas es de un 8,79%}}
Usaremos la distribución binomial para calcular la probabilidad de que exactamente 3 de las 5 solicitudes sean rechazadas.
La fórmula para la distribución binomial es:
Donde:
-
-
-
-
Sustituyendo estos valores en la fórmula:
Calculamos
Entonces,
Por lo tanto, la probabilidad de que exactamente 3 de las 5 solicitudes sean rechazadas es del 8.79%.
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