What is the minimum sample size required to estimate a popul

What is the minimum sample size required to estimate a population mean with 90% confidence when the desired margin of error is D = 1.25? The standard deviation in a preselected sample is 8.5.

Solution

Note that      
      
n = z(alpha/2)^2 s^2 / E^2      
      
where      
      
alpha/2 = (1 - confidence level)/2 =    0.05  
      
Using a table/technology,      
      
z(alpha/2) =    1.644853627  
      
Also,      
      
s = sample standard deviation =    8.5  
E = margin of error =    1.25  
      
Thus,      
      
n =    125.1043293  
      
Rounding up,      
      
n =    126   [ANSWER, A]