Lesser developed countries experiencing rapid population growth often face severe traffic control problems in their large cities. Traffic engineers have determined that elevated rail systems may provide a feasible solution to these traffic woes. Studies indicate that the number of maintenance-related shutdowns of the elevated rail system in a particular country has approximately a Poisson distribution with a mean equal to 6.5 per month.

(a)Find the probability that at least five shutdowns of the elevated rail system will occur next month in the country.

(b)Find the probability that in the next 3 months, only one month has four shutdowns.