A sample of 1300 voters is asked if they would vote for cand

A sample of 1300 voters is asked if they would vote for candiate A if the election were held today. If the population proportion of votes who would vote for candidate A if the election were held today is 0.53 , what is 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?

Thank you!!

Solution

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