A quality control engineer at a pharmaceutical company is in

A quality control engineer at a pharmaceutical company is interested in

verifying the mean aspirin content in the company\'s aspirin tablets. Assuming aspirin content

follows a normal distribution with standard deviation of 5 mg, how large of a sample must

be taken in order for the margin of error to be within 1 mg with 99% confidence?

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 =    5  
E = margin of error =    1  
      
Thus,      
      
n =    165.872415  
      
Rounding up,      
      
n =    166   [ANSWER]