The voters in california are voting for a new governor. of the voters in california, a propor-
tion p will vote for frank, and a proportion 1 - p will vote for tony. in an election poll, a
number of voters are asked for whom they will vote. let xi be the indicator random variable
for the event "the ith person interviewed will vote for frank." that is, xi = 1 if the ith
person interviewed will vote for frank, and xi = 0 if the ith person interviewed will not vote
for frank. a model for the election poll is that the people to be interviewed are selected in
such a way that the indicator random variables x1, are independent and have a ber(p)
distribution.
(a) suppose we use (average should have a line over the xn) xn to predict p. according to chebyshev's inequality, how large should n be (how many people should be interviewed) such that the probability that x
n is within 0: 2 of the "true" p is at least 0: 9? (hint. solve this rst for p = 1=2, and use the
fact that p(1 - p) < = 1/4 for all 0 < =p < =1.)
(b) answer the same question, but now (average) xn should be within 0.1 of p.
(c) answer the question from part (a), but now the probability should be at least 0.95.
(d) now compute the number n so that xn will be within 0.02 of p with probability 0: 95.
(this is often the standard level of accuracy for polling.)