Final answer:
To calculate the waiting time for a furniture delivery using a uniform distribution, use the expected value formula (a + b) / 2. With delivery between 10 a.m. and 2 p.m., the expected wait time would be 2 hours from the 10 a.m. start time.
Step-by-step explanation:
The scenario provided discusses the delivery service of Richard's Furniture Company, which delivers furniture uniformly between 10 a.m. and 2 p.m. For customers, an important aspect of any delivery service is the ability to track their delivery. If customers are interested in calculating how long they have waited for their delivery since the 10 a.m. start time, they will need to understand the concept of the uniform distribution in mathematics, specifically in probability and statistics. This uniform distribution can be used to model the scenario as it involves a continuous random variable representing the delivery time.
To calculate the waiting time in hours past the 10 a.m. start time for an individual delivery, customers can use the formula for the expected value of a uniform distribution, which is (a + b) / 2, where 'a' is the start time and 'b' is the end time. For Richard's Furniture Company, a = 0 (since 10 a.m. is the zero point) and b = 4 hours (since 2 p.m. is 4 hours after 10 a.m.). Therefore, the expected value for the waiting time would be (0 + 4) / 2 = 2 hours. This calculation indicates that, on average, customers can expect to wait about 2 hours for their delivery after 10 a.m.