2. A consumer agency that proposes that lawyers' rates are too high wanted to estimate the mean hourly rate for all lawyers in New York City. In 2020 a sample of 100 lawyers taken from New York City showed that the mean hourly rate charged by them is $425. The population standard deviation of hourly charges for all lawyers in New York City is $115. a) What is the point estimate for the corresponding population mean? b) What distribution (z or t) you need to use to construct the confidence interval and why? c) Construct a 99% confidence interval for the mean hourly charges for all lawyers in New York City. d) What is the margin of errors? 3. We continue with the previous problem 2. According to the U.S. Bureau of labor Statistic all lawyers in New York City charged on average $400 per hour in 2010. Find the p-value for the test of hypothesis with the alternative hypothesis that the mean hourly rate in 2020 is bigger than $400. a) State the null and the alternative hypothesis. b) Draw a distribution and show p-value on it. Find the p-value