Exit polling is a popular technique used to determine the outcome of an election prior to results being tallied. Suppose a referendum to increase funding for education is on the ballot in a large town (voting population over 100,000). An exit poll of 300 voters finds that 144 voted for the referendum. How likely are the results of your sample if the population proportion of voters in the town in favor of the referendum is 0.51? Based on your result, comment on the dangers of using exit polling to call elections.

A) The probability is 0.0838.

B) the use of exit polling to call elections is dangerous event.

Step-by-step explanation:

We are given;

A referendum to increase funding for education is on the ballot in a large town (voting population over 100,000)

Number voters in an exit poll; N = 300

Number of voters who favored referendum; X = 144

probability of sample proportion if the population proportion of voters in the town in favor of the referendum; p = 0.51

Sample proportion of voters who favored referendum is given as,

p' = 144/300

p' = 0.47

Using the central limit theorem, the sampling distribution of proportion for a large sample size of 300,follows normal distribution with mean same as population proportion and standard deviation given by the formula;

s = √(p(1 - p)/n

s = √(0.51(1 - 0.51)/300

s = 0.028862

np = 300 x 0.51 = 153

n(1 - p) = 300(1 - 0.51)

n(1 - p) = 147

np and n(1 - p) are both greater than 5,thus;

the probability of sample proportion if the population proportion of voters in the town in favor of the referendum is 0.51 is expressed as follows,

P(p > p') = P(Z < (p'- p)/s)

P(p > p') = P(Z < (0.47 - 0.51)/0.028862)

P(p > p') = P(Z < - 1.386)

From the table i attached, the z value is 0.0838

Thus, the probability of occurrence of sample proportion given the population proportion of voters in the town in favor of the referendum of 0.51 is 0.0838

Based on these results, it is observed that the exit poll proportion result is a rare event with very less probability of occurrence. Hence, if translated for entire population, it might lead to incorrect results.

Hence the use of exit polling to call elections is dangerous event.

x^2 + 81

we can factor this using difference of square binomials.

rewrite the equation:

x^2 - (-81)

factor:

(a^2 - b^2) = (√a^2 + √b^2)(√a^2 - √b^2)

(x^2 - (-81) = (x + √-81)(x - √-81)

we can remove the - from under the radical by multiplying it by i.

(x^2 - (-81) = (x + i√81)(x - i√81)

(x^2 - (-81) = (x + 9i)(x - 9i)

we can check our answer by using foil:

x^2 - 9ix + 9ix - 81i^2

x^2 - 81^2

i^2 = -1

x^2 + 81