REALLY NEED HELP WITH THESE.A machine can be adjusted so that under control, the mean amount of sugar filled in a bag is 5 pounds. To check if the machine is under control, a few bags were picked at random and their weights (in pounds) were found to be as follows: 4.87 4.88 4.93 4.97 5.01 5.07 5.08 5.09 5.11 5.11 5.14 5.22 5.24 5.43 a) Identify the variable under consideration. Is it discrete or continuous? b) Construct a box plot. Comment on the shape of the distribution. c) Find the sample mean and the sample SD. d) Suppose these 14 bags were sold to a retailer. She selected 5 of them randomly without replacement and weighed them. What is the probability that exactly two of them will weigh less than 5 lbs. (no need to simplify). A video game has three levels. 80% of the players reach 2nd level. Out of those who reach the 2nd level 75% of them reach the third level. Among those who reach the 3rd level only 50% of them complete the game. a) What is the probability that a randomly chosen player will complete all three levels. b) Suppose 25 players were selected randomly. Let Y be the number of players who completed all three levels. i) How is Y distributed? ii) What is the chance that at least 10 players will complete all three levels?. iii) Find the expected value and the standard deviation of the r.v. Y .Professor Brown bought 4 Math books, 3 Stat books and 2 Econ books. She asked her assistant to shelve those books, who did that in a random order. What is the probability that all the books dealing with the same subject are shelved together? You do not need to simplifyAn electrical system has seven (7) identical components. These components work independently. Probabiity that a component will fail is 0.15. The system works if at least one of them work. a) What is the probability that exactly three of them will fail? b) What is the probability that the system will work?Participants in a race are expected to finish the race in 20 minutes with a sd of 3 minutes. If it has a bell shaped distribution then (a) The fastest 2.5 % of runners finish before what time? (b) What percentage of people will finish in 23 minutes or less? (c) If a person tells you they finished the race in ten minutes, do you have any reason to doubt his/her claim?Machines A and B produce 30% and 70% respectively of the production of a component intended for the motor industry. From experience, it is known that the probability that machine A produces a defective component is 0.06 while the probability that machine B produces a defective component is 0.02. A component is selected at random from a days production. a) What is the probability that the item is defective? b) Suppose the item was found to be defective, find the probability that it was made by machine A. .