$2023 \_24$ TERM3 Kaseyann Anderson $11 / 25 / 23$ 7:33 PM 8.188 .2 Question 7 of 7 This test: 7 point(s) possible This question: 1 point(s) possible Submit test 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 192 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 0.51 ? 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 0.51 ? The probability that fewer than 192 people voted for the referendum is $\square$ (Round to four decimal places as needed.) Comment on the dangers of using exit polling to call elections Choose the correct answer below A. The result is unusual because the probability that $\hat{p}$ is equal to or more extreme than the sample proportion is greater than $5 \%$. Thus, it is not unusual for a wrong call to be made in an election if exit polling alone is considered B. The result is not unusual because the probability that $\hat{p}$ is equal to or more extreme than the sample proportion is less than $5 \%$. Thus, it is unusual for a wrong call to be made in an election if exit polling alone is considered. C. The result is unusual because the probability that $\hat{p}$ is equal to or more extreme than the sample proportion is less than $5 \%$. Thus, it is unusual for a wrong call to be made in an election if exit polling alone is considered Submit test Search 느 (9) $=$ 7:31 PM 11/25/2023
Solution
Step 1 ：The question is asking for the probability that fewer than 192 people voted for the referendum if the population proportion of voters in favor of the referendum is 0.51.
Step 2 ：This is a binomial distribution problem where the number of trials is the number of voters polled (400), the number of successes is the number of people who voted for the referendum (192), and the probability of success on each trial is the population proportion of voters in favor of the referendum (0.51).
Step 3 ：We can use the cumulative distribution function (CDF) of the binomial distribution to find the probability of getting fewer than 192 successes.
Step 4 ：Let n = 400, p = 0.51, and k = 191.
Step 5 ：Using these values, we find that the probability is approximately 0.1056.
Step 6 ：Final Answer: The probability that fewer than 192 people voted for the referendum is \( \boxed{0.1056} \).
