Give full detailed explanation with answers

1. The following data represent a random sample of 9 (out of 10) on a statistics quiz. The marks are normally distributed with a standard deviation of 2, Estimate the population mean with 90% confidence. (10 points) 7 8 4 6 3 10 9 2. A random sample of 15 hourly wages for restaurant servers (including tips) was drawn from a normal population. The sample mean and sample standard deviation were I - $14.9 and s = $6.75, Can we infer at the 5% significance level that the mean wage for restaurant servers (including tips) is greater than 127 (10 points) 3. A financial analyst is concerned with the return associated with a portfolio of stocks. She draws a random sample of nine monthly returns (expressed as a percentage of the initial investment). These data follow: 2, 5, -6, 10, 1, 2, -3, 0, and 7. Find a 95% confidence interval estimate of the population mean. (10 pts)