A recent study of commuter trains shows that

STA-2023Exam 2Randall Miller IIInstructions: Read every question carefully. To receive full credit for any question, youmust provide the formula(s) used in the problem, show your work, and give the correctanswer both numerically and in reference to the problem, for example, “The meanage of all FIU students is 27 years.” Remember, do not round your calculations until youobtain your final answer and then round to four decimal places. Whenever the questionsays explain, why, of justify, you must provide the correct reasoning as to why youanswered the way you did.1. A recent study of commuter trains shows that they run more than 35 minutes latewith probability equal to .3. If we are using a commuter train that exhibits thesecharacteristics and we randomly select ten days within the past year, what is theprobability that the train is always late (using the formula)? What is theprobability that the train is late more than eight times out of ten (using the table)? STA-2023Exam 2Randall Miller II2. A government study suggests that one in every three telephone calls made bygovernment employees is for non-business purposes. Suppose that a governmentfacility makes 30 million calls per year and that each call costs the taxpayers$3.75 for the use of the communications equipment and for the employee’s time.a. What is the expected number of non-business calls?b. What is the standard deviation?c. What is the expected cost for these calls to the taxpayers for a year? STA-2023Exam 2Randall Miller II3. The number x of people entering the intensive care unit at a particular hospital onany one day possesses a Poisson probability distribution with mean equal to 15persons per day.a. What is the probability that the number of people entering the intensivecare unit on a particular day is equal to 5?b. Less than or equal to 3? STA-2023Exam 2Randall Miller II4. A soft-drink machine can be regulated so that it discharges an average of ounces per cup. If the ounces of fill are normally distributed with standarddeviation equal to .25 ounce, give the setting for so that 8-ounce cups willoverflow only 1% of the time. STA-2023Exam 2Randall Miller II5. The length of life of a type of automatic washer is approximately normallydistributed with mean and standard deviation equal to 3.5 and .75 yearsrespectfully. If this type of washer is guaranteed for one year, what fraction oforiginal sales will require replacement?