Suppose that, in a certain electorate, 40% of electors would vote for the sittin

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

Explanation / Answer

Normal Approximation to Binomial Distribution
Mean ( np ) =1300 * 0.53 = 689
Standard Deviation ( npq )= 1300*0.53*0.47 = 17.9953
Normal Distribution = Z= X- u / sd                   
P(X < 650) = (650-689)/17.9953
= -39/17.9953= -2.1672
= P ( Z <-2.1672) From Standard NOrmal Table
= 0.0151                  
the probability of obtaining less than 650 out of the 1300 that say they would
vote for candidate A if the election were held today is 0.0151

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