Dont use Excel, please

Please keep four digits after the decimal point in your solutions. 1. [25 points] Mount Lyon is company which provides bus transportation services to a University. It received many complaints during the spring semester, and then it conducted a study of the bus system service quality. Their findings show that 10 students arrive at the Engineering Building stop every 2 minutes, and 50% percent of them are headed to the students' residential complex during rush hours. According to the bus schedule, there are supposed to be one bus every 5 minute from Engineering Building to residential complex. Suppose the inter-arrival time between students follows exponential distribution, and all waiting students can be taken by a single bus. a. [5 points] What probability distribution does the 7th student arrival time follow? b. [5 points] What time should we expect the 7th student after a bus leaves? c. [5 points] What probability distribution does the number of waiting students for each bus follow? d. [5 points] What is the average amount of students that each bus is carrying? e. [5 points] What is the probability that a bus carries less than 5 students