2019 saw the first reported case of COVID-19. Scientists from the World Health Organization are tasked with creating protocols for quarantining infected patients. In particular, they must outline the length of time that patients are to be kept in quarantine before they are considered safe to release and no longer contagious to the public. Assume that it is known that the time to recovery has a mean of 14.36 days and variance of 6.82 days.please clearly define any variables and models you use.

Assume that it is known that the time to recovery has a mean of 14.36 days and variance of 6.82 days.Be sure to define clearly any variables and models you use.

(a)Assuming that the time to recovery follows a Normal distribution, find the following: I. An infected patient is selected at random. What is the minimum number of days that they should be quarantined such that there is a 99.9% chance that they will be recovered before release? ii. 100 infected patients are selected at random. What is the probability that their mean time to recovery is no more than 15 days? iii. Suppose 21 patients on a cruise ship simultaneously and suddenly become infected with the virus. With only 2 weeks remaining on their voyage, what is the probability that all patients will be recovered before they return to port, as to not infect anybody on shore when they return on the 15th day? Assume that the patients' recovery is independent of one another.

b) Assume the true distribution of time to recovery is unknown. Given this, consider the following: I. Explain one reason why the Normal distribution might be a poor representation of the true distribution of time to recovery? Briefly explain - ii. Is the probability you calculated in part (1(a)ii) still accurate? Briefly explain - iii. A random sample of 144 infected patients reveals that their mean time to recovery is 15.09days. Is the mean recovery time of these 144 patients unusual? Justify the answer using probabilistic evidence.