Question

The actual proportion of voters who plan to vote for a particular proposition in the next election is 70%, but LaShandra does not know this. LaShandra has been hired by the election campaign to conduct a sample survey to estimate the proportion of voters who will vote for the proposition. LaShandra decides to take a random sample of size 121 from all eligible voters. 33. What is the probability that LaShandra's sample proportion will be within ± 0.03 of the actual population proportion?

Answer 1

Solution

Given that,

p = 0.70

1 - p = 1 - 0.70 = 0.30

n = 121

= p = 0.70

=  [p ( 1 - p ) / n] = [(0.70 * 0.30) / 121 ] = 0.0417

P(0.67 < < 0.73)

= P[(0.67 - 0.70) /0.0417 < ( - ) / < (0.73 - 0.70) / 0.0417]

= P(-0.72 < z < 0.72)

= P(z < 0.72) - P(z < -0.72)

Using z table,   

= 0.7642 - 0.2358

= 0.5284