1. (20 points) In a random sample of 140 observations of workers on a site, 25 were found to be idle. (a) (10 points) Construct a 99% confidence interval for the true proportion of workers found idle, using the large sample confidence interval formula. (b) (10 points) What can we say with 95% confidence about the maximum error if we use the sample proportion to estimate the corresponding true proportion? 2. (10 points) Among 100 fish caught in a large lake, 18 were inedible due to the pollution of the environment. If we use 18/100 = 0.18 as an estimate of the corresponding true proportion, with what confidence can we assert that the error of this estimate is at most 0.065? 3. (20 points) Suppose that we want to estimate what percentage of all bearings wears out due to friction within a year of installation. (a) (10 points) How large a sample will we need to be at least 90% confident that the error of our estimate, the sample percentage, is at most 2.25%? (b) (10 points) How large a sample will we need to be at least 90% confident that the error of our estimate is at most 2.25% if we know that 15% of the bearings in a preliminary sample wears out due to friction within a year of installation