Question

The closing costs on a home mortgage loan is normally distributed with an average of 5.9% with a standard deviation of 1.9%. If a lender wants to claim that it is in the top 3% of lenders with the LOWEST closing costs, what percentage of the loan must they charge?

Answer 1

Answer

We have mean = 5.9 and standard deviation = 1.9

we have to find the x value corresponding to top 3% or 97th percentile.

So, we will use the z formula given as

where we have

Using z score - percentile for normal distribution table, we have to find the z value for 97th percentile

(In the percentile column, looking for 97 value and finding its corresponding z value in the adjacent column)

we get, z = 1.881

Now, setting the given values in the z value formula above, we get

1.881 = (-5.9)/1.9

multiplying both sides by 1.9, we get

1.881*1.9 = (-5.9)*1.............................(on right hand side, 1.9/1.9 becomes 1)

3.5739 = (-5.9)

adding 5.9 on each side, we get

3.5739 + 5.9 = (-5.9)+5.9

9.4739 =

So, required percentage of the loan = 9.47% (rounded to 2 decimals)