MAT 210 Exam 2, Spring 2016

MAT 210 a) Find P(O< x <1/¥ =2) b) Find PO<x< 5 &0<y< 1) c) Arex & v independent? Justify your answer. 6. (Spts) A manufacturing firm claims that the batteries used in their electronic games will last an average of 30 hours. To maintain this average, 16 batteries are tested each month. What conclusion should the firm draw from a sample that has a mean of 27.5 hours and a standard deviation of 5 hours? 7.(10pts) Ifa certain machine has electric resistors of type A having a mean resistance of 3.0 ohms and a standard deviation of 2 ohms, while those of type B have a mean resistance of 2.8 ohms with a standard deviation of 1 ohms. What is the probability that a random sample of 36 resistors of type A will have a mean of at least 0.2 ohms less than the mean resistance of a sample of 49 resistors from type B? 8.(10 pts — 5 pts each) The weekly repair cost (in hundreds of dollars) for a certain machine is arandom variable Y with a probability density function given by fy)= \ —yP forbeye<l elsewhere a) Finde. b) Find the expected value and variance of ¥. 9. (10 pts — 5 pts each)A process yields 10% defective items. If 100 items are randomly selected from the process, what is the probability that the number of defectives a) exceeds 13 7 b) is less than & * 10. (10pts - 5 pts each) The length of time for one keyboard to be manufactured is a random variable having an exponential distribution with a mean of 4 minutes. a) What is the probability that a keyboard is manufactured in less than 3 minutes on at least 4 ofthe next 6 days? b) Find the mean and the standard deviation.