A political pollster is conducting an analysis of sample results in order to makepredictions on election night. Assuming a two-candidate election, if a specific candidate receives 55% ofthe vote in the sample, that candidate will be forecast as the winner of the election. If you select arandom sample of 100 voters, what is the probability that a candidate will be forecast as the winner when

a. The population percentage of her vote is 50.1%?

b. The population percentage of her vote is 60%?

c. The population percentage of her vote is 49% (and she will lose the election)?

d. If the sample size is increased to 400, what are your answers to (a) through (c)?

I am also having some trouble with this question:

Could you explain why the shapes are how they are?

The US Census Bureau announced that the mean sales price was $345,800. Assume that the standard deviation of the prices is $90,000.

a. If you select samples of n=4, describe the shape of the sampling distribution, X. (the icon indicates x-bar)

b. If you select samples of n=100, describe the shape of the sampling distribution of X.

c. If you select a random sample of n=100, what is the probability that the sample mean will beless than $370,000?

d. If you select a random sample of n=100, what is the probability that the sample mean will bebetween 350,000 and 365,000?