Question

Suppose that, in a certain electorate, 40% of electors would vote for the sitting Member of Parliament if an election were held today. The MP commissions a survey of 400 randomly selected electors within her electorate, who are asked who they would vote for if they were to vote today. If all participants answer honestly, what is the approximate probability that more than 44% of respondents would say that they intend to vote for the MP? [Hint: Note that n is large. What is the approximate distribution of the proportion of voters ('p-hat') who intend to vote for the MP?] 0.129 0.484 0.051 0.871 0.949

Answer 1

Solution

Given that,

p = 40% = 0.40

1 - p = 1 - 0.40 = 0.60

n = 400

= p = 0.40

=  [p( 1 - p ) / n] = [(0.40 * 0.60) / 400 ] = 0.0245

P( > 0.44) = 1 - P( < 0.44)

= 1 - P(( - ) / < (0.44 - 0.40) / 0.0245)

= 1 - P(z < 1.6327)

Using z table

= 1 - 0.949

= 0.051