Customers arrive at a certain facility according to a Poisson process of rate A. Suppose that it is known that five customers arrived in the first hour. Each customer spends a time in the store that is a random variable, exponentially distributed with parameter a and independent of the other customer times, and then departs. What is the probability that the store is empty at the end of this first hour

The weibull distribution is widely used in statistical problems relating to aging of solid insulating materials subjected to aging and stress. use this distribution as a model for time (in hours) to failure of solid insulating specimens subjected to ac voltage. the values of the parameters depend on the voltage and temperature; suppose α = 2.5 and β = 190. (a) what is the probability that a specimen's lifetime is at most 250? less than 250? more than 300? (round your answers to four decimal places.) at most 250 less than 250 more than 300 (b) what is the probability that a specimen's lifetime is between 100 and 250? (round your answer to four decimal places.) (c) what value is such that exactly 50% of all specimens have lifetimes exceeding that value? (round your answer to three decimal places.) hr