The prices of condos in a city are normally distributed with

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?

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?

Solution

A)

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.0668      
          
Then, using table or technology,          
          
z =    -1.500055603      
          
As x = u + z * s,          
          
where          
          
u = mean =    90000      
z = the critical z score =    -1.500055603      
s = standard deviation =    28000      
          
Then          
          
x = critical value =    47998.44312   [ANSWER]

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b)

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.9821      
          
Then, using table or technology,          
          
z =    2.099191761      
          
As x = u + z * s,          
          
where          
          
u = mean =    90000      
z = the critical z score =    2.099191761      
s = standard deviation =    28000      
          
Then          
          
x = critical value =    148777.3693   [ANSWER]