Over the course of a year, the manager of Motel St-Jacques, located in Brossard, Quebec, has noticed that on average, 170 rooms will be rented out every night, with a standard deviation of 10 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 155 rooms are rented.
b) More than 190 rooms are rented.
c) More than 164 rooms are rented.
d) Between 162 and 188 rooms are rented.