Binomial Distributions of Exit Polling
Statistical Topic: 
The binomial distribution is a population distribution for a categorical variable that has only two responses. Examples of this type of categorical variable with its two responses are tossing a coin with heads and tails possible, answering a survey question with a yes or no response, determining which way to turn at a stop sign as left and right, etc.  An experiment is called a binomial if it has a fixed number of trials, if each trial results in only two mutually exclusive outcomes, if these outcomes are independent and if the probability for each outcome is the same for every trial.  This binomial probability distribution can be used to determine the probability for any value of the random variable defined as the number of successes.
Student Issue:
Exit polling has been a controversial practice in recent elections since early release of results is thought to affect voters who have not yet voted.  Since voters would be asked if they were in favor of banning the release of information before polls closed or not, this categorical variable fits the properties of a binomial experiment. 
Statistical Techniques: 
    1. Using the properties of a binomial experiment, confirm that asking 10 people whether they are in favor of banning exit polling or not fits ALL the properties. Define your random variable for this experiment and determine what is success and failure (hint you might make success fit problem 2). 

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    2. Suppose 50% of all voters asked were in favor of banning the release of information from exit polls until after all polls had closed, compute the probabilities of having  0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10 voters are in favor of the ban. Draw the probability distribution for the random variable of number of voters asked.  Make sure to label the x and y axis.  What is the mean and standard deviation for this distribution?

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    3. What is the probability that more than 6 people favor the ban?  What is the probability at least 6 people favor the ban? What is the probability that more than 3 people and less than 7 favor the ban?

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    4. Suppose 90% of 10 voters were in favor of the ban, compute the probabilities of having  0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10 voters are in favor of the ban. Draw the probability distribution for this random variable.  Make sure to label the x and y axis.  What is the mean and standard deviation for this distribution?  How does this distribution compare to the one draw in problem 2?

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    5. Suppose 90% of 100 voters were in favor of the ban, draw the probability distribution for all the probabiilties from 0 to 100 people favoring the ban. Again label all axes and find the paramerters for this distribution. 

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Social Commentary:
    1. What is your opinion about exit polling?  
    2. Is banning exit polling and releasing such information a violation of the "free speech" amendment?