Customers arrive at a restaurant according to a Poisson distribution at a rate of 20 customers per hour. The restaurant opens for business at 11:00 am. (Assume that customers will stay long enough). (a) Find the probability of having 20 customers in the restaurant at 11:12 am given that there were 18 customers at 11:07 am. (b) Given that the last customer arrived at 11:25 am, find the probability that the next customer will arrive between 11:28 and 11:30 am. (Hint: use the relation between Poisson and Exponential distribution)