Residents in central Nassau County are petitioning for a traffic signal at a certain intersection. Engineers are studying the flow of vehicles through this intersection during the morning and evening weekday "rush hour". Existing traffic flow models must be re-examined, given the high proportion of persons working from home due to Covid. Before the pandemic, many took the train into NYC on weekdays. The new traffic flow model shows that flow of vehicles through this intersection is a Poisson process with mean rate of 7 vehicles per minute. a) Find the probability that in the next minute exactly 5 vehicles pass through the intersection. Express solution symbolically (showing the formula used), then evaluate to 8 decimal places. Find the probability that in the next minute at most 2 vehicles pass through the intersection. Express solution symbolically (showing the formula used), then evaluate to 8 decimal places.