Final answer:
a. The practical capacity of the carwash when the average waiting time of 5 minutes is considered acceptable is approximately 3.99 minutes. b. If the service time is reduced to 2.5 minutes, the practical capacity would be increased to approximately 6.99 minutes. c. The ultimate capacity of the carwash would be determined by the service time alone, which is 3.0 minutes.
Step-by-step explanation:
a. The practical capacity of the carwash can be determined by calculating the number of cars that can be serviced within the acceptable waiting time. To do this, we need to find the Z-score corresponding to the acceptable waiting time of 5 minutes. Using the formula Z = (X - μ) / σ, where X is the waiting time, μ is the mean, and σ is the standard deviation, we can find the Z-score. The formula can be rearranged to solve for X: X = (Z * σ) + μ. Plugging in the Z-score, standard deviation, and mean, we get X = (1.33 * 0.75) + 3.0 = 3.99 minutes. Therefore, the practical capacity of the carwash when the average waiting time of 5 minutes is considered acceptable is approximately 3.99 minutes.
b. If the service time is reduced to 2.5 minutes, we can follow the same process as in part a to find the practical capacity. Plugging in the new service time into the formula, we get X = (5.33 * 0.75) + 3.0 = 6.99 minutes. Therefore, the practical capacity would be increased to approximately 6.99 minutes.
c. The ultimate capacity of the carwash would be determined by the service time alone, without consideration for the waiting time. In this case, we can use the average service time of 3.0 minutes as the ultimate capacity.