You have collected a sample of size n=30 concentration measurements from a normal population with unknown mean and known standard deviation of 3.0 mg/ml.

a) To obtain your individualized sample measurements for this problem, first run a Matlab command or python script or use any other computing method to generate 30 random numbers between 70.0 and 80.0 mg/ml. For this problem do not worry about the type of continuous distribution (i.e., normal, uniform) these numbers follow as these 30 random numbers are simply serving as your individualized sample measurements for the sake of this exam problem. Copy and paste your own code or the screenshot of your execution of the Matlab command to generate these 30 measurements. Write 30 measurements in a 6X5 table below.

b) Calculate the mean and variance of your individualized sample measurements.

c) Determine an interval of concentrations ( , + ) such that the probability that the true value of the population mean lies in the interval is 0.94.

d) Now do part c if you are told that the population standard deviation was not known.