Final answer:
The time period to acknowledge a customer walking through the doors to make the rate of purchase 70 percent is within 2.41 minutes of the previous customer.
Step-by-step explanation:
The time period to acknowledge a customer walking through the doors, in order to make the rate of purchase 70 percent, can be determined by using the formula for the 70th percentile. According to the information provided, 70 percent of customers arrive within 2.41 minutes of the previous customer. Therefore, the time period to acknowledge a customer should be within 2.41 minutes of the previous customer.