I am quite pressed for time! Would anyone be able to help me with the following question?

1. (21 pts) A chemical plant is discharging a certain toxic chemical into a river. Officials from the Environment Protection Agency determine that the maximum safe discharge of this chemical is 1.5 ounces per week. In an attempt to monitor the plant's compliance, they measure the actual amount of discharge each week. In five randomly selected weeks, the actual discharges are 2.8, 1.3, 4.1, 1.8 and 2.5 ounces. Assume that the amount of discharge is normally distributed. (a) (3 pts) What is the sample mean of these discharges? As the weekly discharge is assumed normally distributed, which one, the sample mean or the sample median, do you recommend for a point estimate of the true average weekly discharge? Why? (b) (2 pts) What is the sample standard deviation? Is it unbiased for the population standard deviation? (c) (1 pt) What is the standard error of the mean? (d) (2 pts) Assume that the amount of discharge is normally distributed, what is the sampling distri- bution of the sample mean X? Give its name, mean and standard deviation. (e) (2 pts) Construct a 99% confidence interval for the average weekly discharge of the plant. (f) (3 pts) How do you interpret the confidence level 99%, in a hypothetical context that a large number of samples are taken and 99% confidence intervals constructed? (g) (2 pts) Say Alex calculates a 90% CI as (1.48, 3.53). Can he conclude that "we are 90% confident that the discharge next week will be between 1.48 and 3.53 ounces"? Explain briefly. (h) (4 pts) Conduct an appropriate hypothesis test to determine whether the plant is in compli- ance with the standard. Set up the null hypothesis and a one-sided alternative, and state your conclusion of the test. Use a = 0.01. Which type of error, Type I or Type II, might have been made? (i) (2 pts) Construct a 99% confidence interval for the population standard deviation o of the weekly discharge