Only question12,14 and 15.

11) A Web server has five major components that must all function in order for it to operate as intended. Assuming that each component of the system has the same reliability. what is the minimum reliability each one must have in order for the overall system to have a reliability of .98? 12) Hoping to increase the chances of reaching a performance goal. the director of a research project has assigned three separate research teams the same task. The director estimates that the team probabilities are .9. .8. and .7 for successfully completing the task in the allotted time. Assuming that the teams work independently, what is the probability that the task will not be completed in time? 13) An electronic chess game has a useful life that is exponential with a mean of 30 months. Determine each of the following: a) The probability that any given unit will operate for at least (1) 39 months. (2) 48 months. (3) 60 months. b) The probability that any given unit will fail sooner than (1) 33 months. (2) 15 months. (3) 6 months. c) The length of service time after which the percentage of failed units will approximately equal (1) 50 percent. (2) 85 percent. (3) 95 percent. (4) 99 percent. 14) A manufacturer of programmable calculators is attempting to determine a reasonable tree-service period for a model it will introduce shortly. The manager of product testing has indicated that the calculators have an expected life of 30 months. Assume product life can be described by an exponential distribution. a. If service contracts are offered for the expected life of the calculator. what percentage of those sold would be expected to fail during the service period? b. What service period would result in a failure rate of approximately 10 percent? 15) Lucky Lumen light bulbs have an expected life that is exponentially distributed with a mean of 20.000 hours. Determine the probability that one of these light bulbs will last a. At least 24.000 hours. b. No longer than 4.000 hours. c. Between 4.000 hours and 24.000 hours