Suppose the average monthly mortgage payment in a city, including principal and interest, is $782 with a standard deviation of approximately $180. if the mortgage payments are assumed to be normally distributed, find the probability that a randomly selected monthly payment is between $600 and $1100.

The probability is 0.8054.

We start out finding the z-value associated with each end of this interval, using the formula
z=(X-μ)/σ

z=(600-782)/180=-182/180=-1.01

Using a z-table (http://www.z-table.com) we see that the area to the left of, less than, this is 0.1562.

For the upper end:
z=(1100-782)/180=318/180=1.77

Using a z-table, we see that the area to the left of, less than, this is 0.9616.

We want the area between them, so we subtract:
0.9616-0.1562 = 0.8054