Question

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?

Answer 1

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%