The number of trucks to unload merchandise to a supermarket is a v.a. with distribution Poisson. If 95.95% of the time the number of trucks arriving per hour is greater than or equal to 2, 87.53% is greater than or equal to 3 and 73.49% is greater than or equal to 4. The supermarket has room for unload a maximum of three trucks at a time. a) If the downloads begin at six in the morning and each of them lasts at least one hour, what is the probability that the download site is full at 6.30am? b) Identify the probability distribution of time to first arrival and determine the probability that after 25 minutes the first truck will arrive.