According to a recent report, the federal government is requiring local officials to enforce a 100 kilometer/hour speed limit within their jurisdictions. Accordingly, any province may be in jeopardy of losing millions of dollars in federal road funds if more than 60% of its vehicles are found to be exceeding the speed limit. In one province, 70 radar surveys are conducted each year at a total of 50 different sites in order to estimate the proportion p of the vehicles exceeding the 100 kilometers per hour. Each of the samples involve at least 500 vehicles.

1. How large of a sample should be selected at site #39 in order to estimate p to within 3% with 90% confidence. Last year approximately 60% of all vehicles exceeded the limit.
2. The average speed of vehicles on major expressways is also of interest to the government. How large of a sample would be necessary at site #39 in order to estimate the mean to within .5 km. with 90% confidence. Assume the standard deviation of speeds is approximately 5km/hr.
3. Set up a 95% confidence interval estimate of the true average speed of vehicles on the major highways if the 70 surveys mentioned yield a sample mean equal to 110 kilometers/hour and a standard deviation equal to 6 kilometers/hour.