Suppose a brewery has a filling machine that fills 12-ounce bottles of beer. It

Question

Suppose a brewery has a filling machine that fills 12-ounce bottles of beer. It is known that the amount of beer poured by this filling machine follows a normal distribution with a mean of 12.27 ounces and a standard deviation of 0.04 ounce. The company is interested in reducing the amount of extra beer that is poured into the 12 ounce bottles. The company is seeking to identify the highest 1.5% of the fill amounts poured by this machine. For what fill amount are they searching? Round to the nearest thousandth. 12.087 oz 12.357 oz 12.183 oz 11.913 oz

Explanation / Answer

First, we get the z score from the given left tailed area. As          
          
Left tailed area = 1 - 0.015 = 0.985      
          
Then, using table or technology,          
          
z =    2.170090378      
          
As x = u + z * s,          
          
where          
          
u = mean =    12.27      
z = the critical z score =    2.170090378      
s = standard deviation =    0.04      
          
Then          
          
x = critical value =    12.357 [answer, B]      

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