In January 2011, the average monthly rental rate for one-bedroom apartments in a certain city was $783. Suppose rental rates across all one-bedroom apartments in this city follow approximately a normal distribution, with a standard deviation of $170. Find the approximate proportion of one-bedroom apartments for which the rental rate:
a. is at least $1000 a month.
b. is less than $500 a month.
c. is between $500 and $1000 a month.