:2a. Solution. The EV of the percentage of tickets in the
sample marked with a 4 is (2000/10000) x 100% = 20%. The
fraction of tickets marked with a 4 is .2, and the fraction of
tickets not marked with a 4 is .8. The SD of the corresponding
0-1 box is the square root of .2 x .8 = .16, or .4. The SE of
the number of 4's in a sample of size 100 is 10 x .4 = 4, so the
SE of the percentage of 4's in such a sample is (4/100) x 100% =
4%.
Since
(14 - 20)/4 = -6/4 = -1.5 and (26 - 20)/4 = 1.5,

the chance that the percentage of 4's is between 14% and 26% is
equal to the area under the normal curve between -1.5 and 1.5, or
about 87%.