Final answer:
The probability that a person must wait at least 1.5 more hours after noon is the ratio of the remaining delivery window (1.5 hours) to the total remaining time (2 hours).
Step-by-step explanation:
Considering the information provided, we can determine the probability that a person must wait at least 1.5 more hours if it is now past noon on a delivery day. Since Richard's Furniture Company delivers furniture from 10 a.m. to 2 p.m., the delivery window is 4 hours in total. By noon, half of the delivery window has passed, leaving 2 hours remaining.
For a person to wait at least 1.5 hours for a delivery after 12 p.m., we have to look at the time frame between 12:30 p.m. and 2 p.m. That is a 1.5-hour window within the 2 hours remaining for delivery.
Since the delivery occurs continuously and uniformly, the probability is calculated as the ratio of the time frame in which the person waits at least 1.5 hours to the total remaining delivery time. The probability that a person must wait at least 1.5 more hours for their delivery after noon is the interval of time from 12:30 p.m. to 2 p.m. (1.5 hours) divided by the total remaining time of 2 hours.