Over the course of a year, the manager of Motel St-Jacques, located in Brossard, Quebec, has noticed that on average, 180 rooms will be rented out every night, with a standard deviation of 15 rooms. If it is assumed that the probability distribution for the number of room rentals forms a normal distribution, what is the probability that on a given night:
a) Less than 150 rooms are rented.
b) More than 195 rooms are rented.
c) More than 164 rooms are rented.
d) Between 170 and 200 rooms are rented.