Suppose that yearly health care expense... Suppose that yearly health care expen

Question

Suppose that yearly health care expense... Suppose that yearly health care expenses for a family of four are normally distributed with a mean expense equal to $4,801 and a standard deviation of $402. An insurance company has decided of offer a health insurance premium reduction it a policyholder's health care expenses do not exceed a specified dollar amount What dollar amount should be established if the insurance company wants families having the lowest 33 percent of yearly health care expenses to be eligible for the premium reduction?

Explanation / Answer

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.33      
          
Then, using table or technology,          
          
z =    -0.439913166      
          
As x = u + z * s,          
          
where          
          
u = mean =    4801      
z = the critical z score =    -0.439913166      
s = standard deviation =    402      
          
Then          
          
x = critical value =    4624.154907   [ANSWER]  

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