1. A simple random sample of size n=250 individuals who are currently employed is asked if they work at home at least once per week. Of the 250 employed individuals surveyed, 31 responded that they did work at home at least once per week. Construct a 99% confidence interval for the population proportion of employed individuals who work at home at least once per week. The lower bound is . (Round to three decimal places as needed.)

2. A simple random sample of size n=12 is drawn from a population that is normally distributed. The sample mean is found to be x=57 and the sample standard deviation is found to be s=20. Construct a 95% confidence interval about the population mean.
The lower bound is
The upper bound is
(Round to two decimal places as needed.)

3. In a random sample of 49 audited estate tax returns, it was determined that the mean amount of additional tax owed was $3443 with a standard deviation of $2568. Construct and interpret a 90% confidence interval for the mean additional amount of tax owed for estate tax returns.

The lower bound is $ (Round to the nearest dollar as needed.)