Subject: Statistical inference The Omicron variant of the COVID-19 has been found to be very infectious. The mathematicians at SZABIST Islamabad in collaboration with a local research center have found its cell size to be an important factor in it being too infectious. The cell size, x, is found to be normally distributed with standard deviation of 300 angstroms. The measurements of thirteen cells were taken using a peculiar method and the sample mean was found to be 3978.1 angstroms [1 angstrom = 10-8 cm]. Question #1) Keeping in view the hypothetical scenario, answer the following questions. a) Estimate the mean cell size of the omicron cells using point estimate b) Find the 98% confidence interval for the mean particle size for this batch of omicron cells. c) Do you think that the results will change if you apply central limit theorem? Please explain