Question 1: (10 Marks: 4+4+2 ) The amount of engine oil sold daily at a service station is uniformly distributed with minimum of 2000 liters and a maximum of 5000 liters. a. Find the probability that daily sales fall between 2500 and 3000 liters? b. What is the probability that the service station will sell at least 4000 liters? (y400 c. What is the probability that the station will sell exactly 2500 liters? P(x=20 Question 2: (8 Marks) Urn A tontaing 4 white marbles and 6 black marbles and Jm B)contains 5 white marbles and 2 black marbles. A marble is randomly selected from Urn A and placed in Um B. Then a marble is randomly selected from Urn B. What is the probability that the marble selected is black. Question 3: (12 Marks: 3+3+3+3) Past records show that 95% of female students who were register for the SAT examination pass it and 80% of the male students who registered for the SAT passed. This vear 60% of the students registered are males. a. What is the probability that a randomly selected student this year will be a female who will pass the SAT exam? b. What is the probability that a randomly selected student this year will be a male who will pass the SAT exam? C. What is the probability that a randomly selected student registered this vear will pass the SAT Exam. d. If a student is randomly selected from those who pass the STAT exam, what is the probability that the student selected will be male? Question 4: (12 Marks: 4+4+4) Assume that each of your calls to a popular radio station has a probability of 0.02 of connecting, that is, of not obtaining a busy signal. Assume that your calls are independent. a. What is the probability that your first call that connects is your 10th call? b. What is the probability that it requires more than five calls for you to connect? c. What is the mean number of calls needed to connect? Question 5: (14 Marks: 44344+3) The lifetime of a television unit is approximately normally distributed with mean 10 years and standard deviation 2.5 years. a. The manufacturer wants to give a guarantee period where any unit failing during this period is replaced at no extra cost. If the manufacturer wants to keep the percentage of replaced unit to no more than 5% of the units sold, How long would the guarantee be good for? b. If you buy one of these television units today, what is the probability that it will last. more than 11.1 years