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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 the probability that the sample unemployment rate is at most 5%.
c) Assume the population proportion, p, is unknown. Describe the sampling distribution of p based on the most recent sample.
d) Based on the most recent sample, find the probability that the sample proportion will lie within 0.005 of the true proportion p of people who are unemployed
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