You Want It Motor Company wants to estimate the percentage

. You Want It Motor Company wants to estimate the percentage of new cars coming off their assembly line that fail the final Quality inspection to within ±1%, with 95% confidence. For planning purposes they use 12%, the percentage reported for their 2010 model. How many cars will they have to sample?

A             1825

B             2267

C             4057

D             7007

E              16227

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 =    0.01  
p =    0.12  
      
Thus,      
      
n =    4056.580515  
      
Rounding up,      
      
n =    4057   [ANSWER C]