The operations manager of a plant making cellular telephones

The operations manager of a plant making cellular telephones wants to estimate the time to assemble the telephone. She knows that the standard deviation is 15 seconds. How large a sample of workers should she take to estimate the mean assembly time to within 2 seconds with 95% confidence?

Solution

Note that      
      
n = z(alpha/2)^2 s^2 / E^2      
      
where      
      
alpha/2 = (1 - confidence level)/2 =    0.025  
      
Using a table/technology,      
      
z(alpha/2) =    1.959963985  
      
Also,      
      
s = sample standard deviation =    15  
E = margin of error =    2  
      
Thus,      
      
n =    216.0820587  
      
Rounding up,      
      
n =    217   [ANSWER]