Question

the fore and aft marina is located on the ohio river near madison, indiana. fore and aft currently operates a docking facility where only one boat at a time can stop for gas and servicing.the manager of the fore and aft marina wants to investigate the possibility of enlarging the docking facility so that two boats can stop for gas and servicing simultaneously. assume that the arrival rate is 4 boats per hour and that the service rate for each server is 8 boats per hour. (round your answers to four decimal places.)(a)what is the probability that the boat dock will be idle?

Answer 1

In this case, the probability is 0.5 or 50%. To find the probability that the boat dock will be idle, calculate the utilization factor as the ratio of the arrival rate to the service rate. Then, subtract the utilization factor from 1 to get the probability of the boat dock being idle.

Step-by-step explanation:

To find the probability that the boat dock will be idle, we need to calculate the utilization factor of the docking facility. The utilization factor is defined as the ratio of the arrival rate to the service rate. In this case, the arrival rate is 4 boats per hour and the service rate for each server is 8 boats per hour. So, the utilization factor is 4/8 = 0.5.

The probability that the boat dock will be idle can be calculated using the formula: idle_prob = (1 - utilization_factor). In this case, the idle_prob = (1 - 0.5) = 0.5.

Therefore, the probability that the boat dock will be idle is 0.5 or 50%.