According to the data, the weight of a randomly selected checked-in luggage has a normal distribution with a mean of 50 lbs and a standard deviation of 11.3 lbs. Let X be the weight of a randomly selected checked-in luggage and let S be the total weight of a random sample of size 10. 1. Describe the probability distribution of X and state its parameters and : X~N and find the probability that the weight of a randomly selected checked-in luggage is between 27 and 53 lbs. 0.2x (Round the answer to 4 decimal places) 2. Use the Central Limit Theorem the original population is normally distributed to describe the probability distribution of S and state its parameters g and org: (Round the answers to 1 decimal place) ~N (HS 50x, s=3. x and find the probability that the total weight of a sample of 10 randomly selected checked-in luggages is less than 478 lbs. (Round the answer to 4 decimal places)