The fill volume of plastic bottles of liquid dishwashing det

The fill volume of plastic bottles of liquid dishwashing detergent is normally distributed with a variance of 8.7 fluid ounces. If we want to estimate the average fill volume with a margin of error of 0.5 with a level of confidence of 99%, how many detergent bottles should we randomly sample?

45

2010

16

231

Solution

Note that      
      
n = z(alpha/2)^2 s^2 / E^2      
      
where      
      
alpha/2 = (1 - confidence level)/2 =    0.005  
      
Using a table/technology,      
      
z(alpha/2) =    2.575829304  
      
Also,      
      
s = sample standard deviation = sqrt(8.7) =   2.949576241  
E = margin of error =    0.5  
      
Thus,      
      
n =    230.8944017  
      
Rounding up,      
      
n =    231   [ANSWER, D]