:5a. Solution. 20% of the tickets in the sample are marked
with a 4, which will be the center of the confidence interval.
To find the SE of the percentage of 4's in a sample of size 100,
we begin by creating a new population by replacing every 4 with a
1 and every 4 with a 0. This gives us a 0-1 population and a 0-1
sample. Estimating the (new) 0-1 box by the (new) sample
average, we get
box SD = square root of .2 x .8 = (.16)^(1/2) = .4

SE for the sum = .4 x square root of 100 = .4 x 10
= 4

SE for % = 4/100 x 100% = 4%,

so an approximate 99.7% confidence interval is given by
20 +/ (3x4%) = 20 +/ 12%. & &I