Question
A cashier counted the number of customers
in their line every minute for 30 minutes.
in their line every minute for 30 minutes.
Ask by Mills Todd. in the United States
Jan 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
La probabilidad de que haya exactamente 2 clientes en la fila es
Solution
Para encontrar la probabilidad de que haya exactamente 2 clientes en la fila, utilizamos la información proporcionada.
-
Condiciones conocidas:
- Se contaron los clientes en la fila cada minuto durante 30 minutos.
- La probabilidad de que haya exactamente 2 clientes en la fila es
.
-
Cálculo de la probabilidad:
- La probabilidad
se puede simplificar dividiendo el numerador y el denominador por 3:
- La probabilidad
Por lo tanto, la probabilidad de que haya exactamente 2 clientes en la fila es:
En resumen, la probabilidad de que haya exactamente 2 clientes en la fila es
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Simplify this solution Mind Expander
To find the probability of having exactly 2 customers in line during the observation period, we can use the formula for probability:
In this case, the number of favorable outcomes for having exactly 2 customers counts as 9 (since it’s been observed 9 times in 30 minutes). Therefore,
This means there’s a 30% chance that at any given minute, the cashier will see exactly 2 customers in line!
When it comes to probability distributions, the Poisson distribution might come in handy here. It’s used to model the number of times an event occurs in a fixed interval of time. In this case, you could say that the occurrence of customers arriving is like random events, making it perfect for applying this distribution! Just remember, the Poisson formula is:
where
