Alocal bank has requested your with analyzing its operations. the time between arrives at the bank is exponentially distributed with a mean inter-arrival time of 0.05 hours. the office opens at 8: 00 am. a) (10 pt) what is the probability that no customers will arrive at the office by 8: 15 am? b) it is now 8: 35 am. the last customer entered the office at 8: 26 am. i. (5 pt) what is the probability that the next customer will arrive before 8: 38 am? ii. (10 pt) what is the probability that the next customer will not arrive by 8: 40 am? c) (10 pt) what is the average number of arriving customers between 8: 10 and 8: 45 am?