A visit to a hospital emergency room for something as simple

A visit to a hospital emergency room for something as simple as a sore throat could have a mean cost of $327.   Assume that this cost is normally distributed with a standard deviation of $80. What is the cut-off dollar amount if you want to be in the top 3% of the patients?

Solution

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.97      
          
Then, using table or technology,          
          
z =    1.880793608      
          
As x = u + z * s,          
          
where          
          
u = mean =    327      
z = the critical z score =    1.880793608      
s = standard deviation =    80      
          
Then          
          
x = critical value =    477.4634887   [answer]