Please provide an explanation for study purposes

Based on current literature, the average incubation period for Covid 19 is 8 days with a standard deviation of 3 days. (a) If we were to take a random sample of 45 patients that were infected with Covid-19, what is the distribution of the sample mean? Total? (3 points) (b) What is the approximate probability that the sample average incubation period is between 7.5 and 9 days? (2 points) (c) What is the approximate probability that the total incubation time for all 45 patients exceeds 380 days. (2 points) (d) What effect does the sample size of 45 have on this problem? What would happen if we increased this sample size to 500? What would happen if we decrease this sample size to 107 (3 points)