The average monthly mortgage payment for all homeowners in a city is $2850. Suppose that the distribution of monthly mortgages paid by homeowners in this city follow an approximate normal distribution with a mean of $2850 and a standard deviation of $420. Find the probability that the monthly mortgage paid by a randomly selected homeowner from this city is
a. less than $1200 

b. between $2300 and $3140

c. more than $3600 

d. between $3200 and $3700