MA260 Statistical Analysis IDirections: Be sure to save an electronic copy of your answer before submitting it to Ashworth College for grading. Unless otherwise stated, answer in complete sentences, and be sure to use correct English, spelling, and grammar. Refer to the \”Assignment Format\” page located on the Course Home page for specific format requirements.NOTE: Show your work in the problems.1. Compute the mean and variance of the following discrete probability distribution.xP(x)2.508.3010.202. The Computer Systems Department has eight faculty, six of whom are tenured. Dr. Vonder, the chair, wants to establish a committee of three department faculty members to review the curriculum. If she selects the committee at random:a. What is the probability all members of the committee are tenured?b. What is the probability that at least one member is not tenured? (Hint: For this question, use the complement rule).3. New Process, Inc., a large mail-order supplier of women’s fashions, advertises same-day service on every order. Recently, the movement of orders has not gone as planned, and there were a large number of complaints. Bud Owens, director of customer service, has completely redone the method of order handling. The goal is to have fewer than five unfilled orders on hand at the end of 95% of the working days. Frequent checks of the unfilled orders follow a Poisson distribution with a mean of two orders. A Poisson distribution is a discrete frequency distribution.Has New Process, Inc. lived up to its internal goal? Cite evidence.4. Recent information published by the U.S. Environmental Protection Agency indicates that Honda is the manufacturer of four of the top nine vehicles in terms of fuel economy.a. Determine the probability distribution for the number of Hondas in a sample of three cars chosen from the top nine.b. What is the likelihood that in the sample of three at least one Honda is included?5. A recent article in the Myrtle Beach Sun Times reported that the mean labor cost to repair a color television is $90 with a standard deviation of $22. Monte’s TV Sales and Service completed repairs on two sets this morning. The labor cost for the first was $75 and it was $100 for the second. Compute z values for each and comment on your findings.6. The mean of a normal distribution is 400 pounds. The standard deviation is 10 pounds.a. What is the area between 415 pounds and the mean?b. What is the area between the mean and 395 pounds?c. What is the probability of selecting a value at random and discovering that it has a value of less than 395 pounds?7. The monthly sales of mufflers in the Richmond, VA area follow the normal distribution with a mean of 1200 and a standard deviation of 225. The manufacturer would like to establish inventory levels such that there is only a 5% chance of running out of stock. Where should the manufacturer set the inventory levels?8. Research on new juvenile delinquents revealed that 38% of them committed another crime.a. What is the probability that of the last 100 new juvenile delinquents put on probation, 30 or more will commit another crime?b. What is the probability that 40 or fewer of the delinquents will commit another crime?c. What is the probability that between 30 and 40 of the delinquents will commit another crime?9. An Air Force study indicates that the probability of a disaster such as the January 28, 1986 explosion of the space shuttle Challenger was 1 in 35. The Challenger flight was the 25th mission.a. How many disasters would you expect in the first 25 flights?b. Use the normal approximation to estimate the probability of at least one disaster in 25 missions.