Question

Suppose the average monthly mortgage payment in the U.S. is $982, the standard deviation is $180, and the mortgage payments are approximately normally distributed. Find the probability that a randomly selected mortgage payment is less than $1,030.

Answer 1

Here's all the information we have:

The average monthly mortgage payment in US is $ 982 and its standard deviation is $180. The payments are approximately normally distributed.

We want to find the probability of a randomly selectad mortgage payment being less than $1,030 P(m<1030|u=982,o=180)

First, we calculate Z = (1030-982)/180 = +0.27

This z value implies 6,75% of all mortgage payment values are located in the interval [$982,$1030]

Since half (50%) of all values are lower than the average value in a normal distribution, this implies that P(m<1030u=982,o=180) = 50% + 6,75% = 56,75% or 0.5675