In a bottle-filling process, the amount of drink injected into 16 oz bottles is

Question

In a bottle-filling process, the amount of drink injected into 16 oz bottles is normally distributed with a mean of 16 oz and a standard deviation of .02 oz. Bottles containing less than 15.95 oz do not meet the bottler’s quality standard. What percentage of filled bottles do not meet the standard? (Round your answer to 2 decimal places.)

In a bottle-filling process, the amount of drink injected into 16 oz bottles is normally distributed with a mean of 16 oz and a standard deviation of .02 oz. Bottles containing less than 15.95 oz do not meet the bottler’s quality standard. What percentage of filled bottles do not meet the standard? (Round your answer to 2 decimal places.)

Explanation / Answer

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    15.95      
u = mean =    16      
          
s = standard deviation =    0.02      
          
Thus,          
          
z = (x - u) / s =    -2.5      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z >   -2.5   ) =    0.006209665 = 0.62% [ANSWER]
          

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