Jamuna Jture park has one parking counter. From previous experience, it is estimated that cars arrive according to Poisson distribution at a rate of 2 every 5 minutes and that there is enough space to accommodate a line of 3 cars. Other arriving cars can wait outside the space, if necessary. It takes 1.5 minutes on an average to serve a customer. However, the service time usually varies according to exponential distribution. Requirements: i- Determine the average time that the counter is free on an 8-hour working day. ii. Determine the probability of having 5 cars in the queue. iii. Determine the probability that a customer shall wait for more than 4 minutes in the queue. iv. Determine the probability that an arriving car will have to wait outside the directed space. v. Now, Jamuna iture park is planning to install automation servicing system that will reduce service time from 1.5 minutes to 1 minute, but increase the cost by TR. 30 per day. Should Jamuna future park introduce the automation servicing system given the cost of goodwill per minute 5 paise? Assume 8 hours working day