The average monthly mortgage payment including principal and interest is $982 in the united states. if the standard deviation is approximately $180 and the mortgage payments are approximately normally distributed, find the probability that a randomly selected monthly payment is more than $1000?

The probability that the monthly payment is more than $1000 will be found as follows;

The payment is normally distributed, thus the z-score will be given by:

Z-score = (x-Mean) / (SD)

Mean=$982

SD=$180

Thus;

Z-score = (1000-982) / 180=0.1

The probability associated with a z-score of 0.1 is 0.5398

Thus the probability that the monthly payment is more than $1000 will be:

P (x<1000) = 1-0.5398=0.4602=46.02%