Exit polling is a popular technique used to determine the ou

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 400 voters finds that 212 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 0.49? Based on your result, comment on the dangers of using exit polling to call elections. How likely are the results of your sample if the population proportion of voters in the town in favor of the referendum is 0.49? The probability that more than 212 people voted for the referendum is . (Round to four decimal places as needed.)

Solution

Note that P(at least x) = 1 - P(at most x - 1).          
          
Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    400      
p = the probability of a success =    0.49      
x = our critical value of successes =    212      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   211   ) =    0.939464615
          
Thus, the probability of at least   212   successes is  
          
P(at least   212   ) =    0.060535385 [ANSWER]