Final answer:
The rate at which customers enter a store is ⅓ customer per minute, and the average time between successive arrivals is 0.6 minutes. For three customers to arrive, it would take on average 1.8 minutes when the store first opens.
Step-by-step explanation:
The student's question involves calculating the rate at which customers are entering a store. Given that 5 customers entered the store over the course of 3 minutes, we can calculate the rate by dividing the total number of customers by the total number of minutes. Therefore, the rate is ⅓ customer per minute or approximately 1.6667 customers per minute.
To address part a of the question, since 5 customers enter in 3 minutes, the average time between two successive arrivals is ⅓ minutes, which simplifies to 0.6 minutes (or 36 seconds) between two successive arrivals.
For part b, considering the calculated average rate, it would take 3 times longer for three customers to enter than it would for one customer. Thus, it would take 1.8 minutes on average for three customers to arrive at the store when it first opens.
In more general contexts like the ones described in the reference information, such calculations can lead to considerations of the exponential distribution to model the time between events, such as customer arrivals. The exponential distribution often applies where events occur independently and at a constant average rate.