If the average home cost $100,000, with a standard deviation of $15,000, what would a home on the 20th percentile rank cost?

To find the cost of a home at the 20th percentile rank, you need to use z-scores and the cumulative distribution function (CDF) of the normal distribution. Here's how you can proceed:

Step 1: Calculate the z-score
The z-score measures the number of standard deviations a value is from the mean. To calculate the z-score for the 20th percentile rank, you need to use the inverse of the CDF function. The formula to calculate the z-score is:

z = (x - μ) / σ

where:
- z is the z-score
- x is the value for which you want to find the percentile rank (unknown to us, we'll call it y for now)
- μ is the mean of the distribution
- σ is the standard deviation of the distribution

In this case, the mean (μ) is $100,000 and the standard deviation (σ) is $15,000. The value of x, which we'll call y, is unknown.

Step 2: Use the inverse CDF function to find the z-score
To find the z-score for a given percentile rank, you need to find the inverse of the CDF function. In other words, you need to find the value of y that corresponds to a cumulative probability of 0.20.

Step 3: Calculate the cost of the home
Finally, once you have the z-score, you can solve the equation from step 1 to find the value of y, which represents the cost of the home at the 20th percentile rank.

Note: To obtain the precise answer, you would typically refer to statistical tables or use statistical software. However, to give you a rough estimate, you can use an online calculator or statistical software to find the z-score and then calculate the cost of the home using the formula in step 1.