please help me answer the following in a step by step process. please use 6 decimals while computing and 4 decimals in the final answer

l. Movies Tonight is a typical video and DVD movie rental outlet for home viewing customers. During the weeknight evenings. customers arrive at Movies Tonight with an arrival rate of 1.25 customers per minute. The checkout cleric has a service rate of 2 customers per minute. ssume Poisson arrivals and exponential service times. ._ a. What is the probabilitv that no customers we in the system? b. Whot is the average humber of customers waiting for service? c. What is the probability that an arriving customer will have to wait for service? a. Whet is the probability that there are 5 customers in the system? 2. Willow Eroak National Bank operates a drive-er teer window that allows customers to complete bank. transactions without getting out of their cars. Oh weekday mornings, arrivals to the drive-up teller window occur at random, with an arrtval rate of 24 customers per hour or 14 customer per minute _ a. What is the mean or expected number of customers that will arrive In a ve-minute period? b. Assume that the Poisson probability distribution can be used to describe the arrival process. Compute: i. the probability that exactly {twill arrive during a ve-minute period ii. the probability that exactly 2 will arrive during a ve-minute period c. Assume that the service times for the dive-up telier follow an exponential probabiittyr distribution with a service rate of 36 customers per hour, at {1.6 customer per minute. Use the exponentiai probability distribution to answer the following questions: i. What is the probability the service time Is one minute or less? ii. What is the probability the service time is two minutes or fess