In the past, the value of houses a local realtor has sold is normally distributed with a mean of $253,000 with a standard deviation of $65,000. How much does a house have to sell for so that the house is in the bottome 20% of lowest selling houses for the realtor? (please express your answer in $'s
http://davidmlane.com/hyperstat/z_table.html
To find the house price that corresponds to the bottom 20% of lowest selling houses for the realtor, we need to calculate the corresponding z-score and then convert it back to the actual house price.
Here's how you can do it step by step:
Step 1: Find the z-score corresponding to the bottom 20% of the standard normal distribution.
The area corresponding to the bottom 20% is 0.20. Using a standard normal distribution table or a calculator, we can find the z-score corresponding to this area.
Step 2: Convert the z-score back to the actual house price.
Once we have the z-score, we can use it to determine the actual house price by using the formula:
house price = (z-score * standard deviation) + mean.
Let's calculate it:
Step 1: Find the z-score corresponding to the bottom 20%.
From the standard normal distribution table or calculator, you can find the z-score corresponding to an area of 0.20, which is -0.8416.
Step 2: Convert the z-score back to the actual house price.
house price = (-0.8416 * $65,000) + $253,000
house price ≈ -$54,824 + $253,000
house price ≈ $198,176
Therefore, a house has to sell for at least $198,176 in order to be in the bottom 20% of the lowest selling houses for the realtor.