Trucks are known to arrive according to a Poisson distribution at a given weight station (checkpoint along a highway to inspect vehicular weights). Trucks are counted in 5-min intervals, and count data (number of trucks in 5-min intervals) are taken in 2,000 of these time intervals. It is noted that no trucks arrive in 100 of these 2000 intervals.

a) What is the probability of observing between 5 and 7 trucks?
b) With the same information, estimate the % of headways that are between 15 and 30 seconds (7 points)