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Hi I am trying to make sure I used the correct formula on the following question to reach my answers:

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The prices of condos in a city are normally distributed with a mean of $90,000 and a standard deviation of $28,000.

a.

The city government exempts the cheapest 6.68% of the condos from city taxes. What is the maximum price of the condos that will be exempt from city taxes?

Answer: $48,000

Found by first subtracting .0668 from .5000 to get .4332. I then located .4332 on the z table provided and found a z score of -1.5. I used the z score to set up the formula -1.5=(x-90,000)/28,000. I solved for x which led me to my answer.

 

b.

If 1.79% of the most expensive condos are subject to a luxury tax, what is the minimum price of condos that will be subject to the luxury tax?

Answer: $148,800

I followed the same procedure on this question. I subtracted .0179 from .5000 and got .4821. I located this number on the z table and found a z score of 2.1. I then used the z score to set up the formula and solve for x. 2.1=(x-90,000)/28,000.

I'm not looking for the answer. I want to understand what I did wrong if I got the answers wrong. I used the Standard normal distribution to find the z-scores and solve for x.

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