6.45 Exit poll An exit poll is taken of 3000 voters in a statewide election. Let X denote the number who voted in favor of a special proposition designed to lower property taxes and raise the sales tax. Suppose that in the population, exactly 50% voted for it.

a. Explain why this scenario would seem to satisfy the three conditions needed to use the binomial distribution.

Identify n and p for the binomial.

b. Find the mean and standard deviation of the probability distribution of X.

c. Using the normal distribution approximation, give an interval in which you would expect X almost certainly to fall, if truly p = 0.50. (Hint: You can follow the reasoning of Example 15 on racial profiling.)

d. Now, suppose that the exit poll had x = 1706. What would this suggest to you about the actual value of p?