3. {15 pts] The time between arrivals of taxis at a busy intersection is exponentially distributed with a mean of E minutes. a. (3 pts} What is the probability that you wait lonuer than one hour for a taxi? I). (2 pts} What is the probability that a taxi arrives within the first 1|] minutes?r e. (5 pts} Suppose you have already been waiting for one how for a taxi. what is the probability that one arrives within the next 11] minutes? d. (5 pts) Determine the leutrth of an interval of time such that the probability of at I least one arrival in the interval is 11.95. (15 pts) The life of a semiconductor laser at a constant power is normally distributed with a mean of 6000 hours and a standard deviation of 600 hours. a. (2 pts) What is the probability that a laser fails before 4,800 hours? b. (2 pts) What is the life in hours that 90% of the lasers exceed? c. (3 pts) What should the mean life equal in order for 99% of the lasers to exceed 10,000 hours before failure? d. (3 pts) A product contains three lasers, and the product fails if any of the lasers fails. Assume the lasers fail independently. What should the mean life equal in order for 99% of the products to exceed 10,000 hours before failure? e. (5 pts) Rework parts (a) and (b) only. Assume that the lifetime is an exponential random variable with the same mean