: the the sample is represented by
400 tickets, 131 marked 1 and the rest marked 0.  We estimate the
SD of the box by that of the sample. So <p>

SD = ( 121/400 x 279/400 )^(1/2) = .46  <p>

The SE for the number of 1's in a sample of size 400 is
approximately 
 	
 .46 x 20 = 9.2  <p>

so the SE for the percentage of 1's in such a sample is  
 	
 (9.2/400) x 100% = 2.3%.  <p>

The EV for the number of 1's is 
 	
 (121/400) x 100% = 30%.  <p>

The z-value corresponding to 70% is approximately 1.05, and <p>

1.05 x 2.3% = 2.4%.  <p>

The 70% confidence interval runs from approximately 
 	
 30 - 2.4 = 27.6%  <p>

to <p>

30 + 2.4 = 32.4%.  <p>

Of the answers, "between 28% and 32%" is the closest. <p>