A machine that produces a major part for an airplane engine

A machine that produces a major part for an airplane engine is monitored closely. In the past, 10% of the parts produced would be defective. With a .95 probability, the sample size that needs to be taken if the desired margin of error is .05 or less is

Select one:

A. 7

B. 33

C. 138

D. 139

Solution

Note that      
      
n = z(alpha/2)^2 p (1 - p) / E^2      
      
where      
      
alpha/2 =    0.025  
       
      
Using a table/technology,      
      
z(alpha/2) =    1.959963985  
      
Also,      
      
E =    0.05  
p =    0.1  
      
Thus,      
      
n =    138.2925175  
      
Rounding up,      
      
n =    139   [ANSWER, D]