Refer to Examples 1 and 2 about the California exit poll, for which the sample size was 3889 and 42.4% of the sample voted for Whitman. We found that after the election, 40.9% voted for Whitman in the population.
a. Identify n and p for the binomial distribution that is the sampling distribution of the number in the sample who voted for Whitman, and use n and p to find the mean and standard deviation of the sampling distribution of the number in the sample who voted for Whitman. (Use the value for p based on the population vote after the election was concluded.)
b. Find the mean and standard deviation of the sampling distribution of the proportion of the people in the sample who voted for Whitman.
c. Compare the mean and standard deviation in part b to the mean and standard deviation in part a.
d. What is the expected shape of both the sampling distribution in part a and in part b? Explain.