The quality assurance department for Duff Cola Inc maintains

The quality assurance department for Duff Cola, Inc. maintains records on the bottling line for two-liter cola bottles. Records indicate that the process follows the normal probability distribution with a mean amount per bottle of 2.01 liters and a standard deviation of 0.025 liters. The QA foreman randomly selects 25 bottles from the bottling line and determines that the mean amount per bottle is 2.005 liters.

     Compute the probability that the sample of 25 bottles would have a mean of 2.005 liters or more.

Solution

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    2.005      
u = mean =    2.01      
n = sample size =    25      
s = standard deviation =    0.025      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    -1      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   -1   ) =    0.841344746 [ANSWER]