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.)

Question 1 (3 points) saved what is the solution for the following system of equations? use any method to solve. y = -x +4 y = x - 2 question 1 options: ( 4 , -2) (2, 1) (3, 1) (3, -2) question 2 (3 points) saved the solution to a system of equations is where the lines intersect. question 2 options: true false question 3 (3 points) which ordered pair is the best estimate for the solution of the system of equations? the graph of the system of equations : y = 3/2x +6 and y=1/4x - 2 question 3 options: (-6, -3) (-6.5, -3.5) (-7, -4) (-7, -3.5) question 4 (3 points) what is the solution for the following system of equations? use any method to solve. 2x + 8y = 4 x = -3y + 5 question 4 options: x = 14, y= -3 x = 2, y = -3 x = -3, y = -3 x = 12, y = 5 question 5 (3 points) solve the following system using any method. 8a - 4b = 20 5a - 8b = 62 question 5 options: a = 5, b = -4 a = 8, b = 4 a = -5, b = -8 a = -2, b = -9 question 6 (3 points) breana is selling tickets to a choral performance. on the first day of ticket sales, she sold 3 senior citizen tickets and 1 child ticket for a total of $38. breana took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. what is the price of a senior citizen ticket? question 6 options: question 7 (3 points) a farmer has 5 times as many cows as pigs. the farmer only has cows and pigs, and he has 168 animals. how many cows does he have? question 7 options: 140 cows 120 cows 50 cows 28 cows question 8 (3 points) how many solutions does the system have? question 8 options: zero one infinitely many question 9 (3 points) what is the solution to the system of equations? graph of x+2y = 6 and y = x question 9 options: (1 , -2) (2, 2) (3, 5) (-2, 2)