Question

The following scenario can be modeled using the Poisson distribution. Identify the value of λ that answers the following question. Customers arrive at a gas station at a rate of 47 customers per hour. What is the average number of customers that would arrive in a 30 minute period?

Answer 1

To find the average number of customers arriving at a gas station in a 30 minute period, the hourly rate of 47 customers is halved, resulting in λ = 23.5 customers for a 30 minute interval according to the Poisson distribution.

Step-by-step explanation:

The subject of this question is Mathematics, specifically pertaining to the Poisson distribution, which is a probability distribution that is used to model the number of times an event occurs in a fixed interval of time or space when these events occur with a known constant mean rate and independently of the time since the last event. In the given scenario, customers arrive at a gas station at a rate of 47 customers per hour. To find the average number of customers that would arrive in a 30 minute period, we would need to calculate the value of λ (lambda), which is the mean number of events in the interval.

To calculate λ for a 30 minute period, we take half of the hourly rate because 30 minutes is half of an hour. Therefore, λ = 47 customers/hour × 0.5 hours = 23.5 customers for a 30 minute period. This would be the average number of customers arriving at the gas station in 30 minutes using the Poisson distribution model.