Question

Exhibit: Condo Price.

The prices of condos in a city are normally distributed with a mean of $100,000 and a standard deviation of $32,000.

Answer the following questions rounding your solutions to 4 digits.

The city government exempts the cheapest 6% of the condos from city taxes. What is the maximum price of the condos that will be exempt from city taxes?

If 2% 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 1

1)

µ=   100000                  
σ =    32000                  
proportion=   0.06                  
                      
Z value at    0.06   =   -1.55   (excel formula =NORMSINV(   0.06   ) )
z=(x-µ)/σ                      
so, X=zσ+µ=   -1.55   *   32000   +   100000  
X   =   50247.24   (answer)          

2)

µ=   100000                  
σ =    32000                  
proportion=   0.98                  
                      
Z value at    0.98   =   2.05   (excel formula =NORMSINV(   0.98   ) )
z=(x-µ)/σ                      
so, X=zσ+µ=   2.05   *   32000   +   100000  
X   =   165719.97   (answer)         

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