Working with sampling distribution and probability.

A southern state has an unemployment rate of 6%. The state conducts monthly surveys in order to track the unemployment rate. In a recent month, a random sample of 700 people showed that 35 were unemployed.

a) If the true unemployment rate is 6%, describe the sampling distribution of p^.

b) Find P(p^ >= 0.05)

c) Assume the population proposal, p, is unknown. Describe the sampling distribution of p^ based on the most recent sample.

d) Find the probability that the sample proportion will lie within 0.05 of the true proportion of people who are unemployed.