The lifetime, in years, of a type of small electric motor operating under adverse conditions is exponentially distributed with λ = 3.500. Whenever a motor fails, it is replaced with another of the same type. Find the probability that fewer than six motors fail within one year. (Round the final answer to three decimal places.)
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The lifetime, in years, of a type of small electric motor operating under adverse conditions is exponentially distributed with λ = 3.500. Whenever a motor fails, it is replaced with another of the same type. Find the probability that fewer than six motors fail within one year. (Round the final answer to three decimal places.)
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- The operator of a pumping station has observed that demand for water during early afternoon hours has an approximately exponential distribution with mean 1000 cfs (cubic feet per second). a)Of the three randomly selected afternoons, what is the probability that on at least two afternoons the demand will exceed 700 cfs?As a data analyst, I received requests at a rate of 1 every 25 minutes, exponentially distributed. Determine the probability that the interval between succeedingmessages is more than 1 hourAt a 911 call center, calls come in at an average rate of one call every two minutes. Assume that the time that elapses from one call to the next has an exponential distribution. On average, how much time occurs between five consecutive calls? Find the probability that after a call is received, it takes more than three minutes for the next call to occur. Ninety percent of all calls occur within how many minutes of the previous call? Suppose that two minutes have elapsed since the last call. Find the probability that the next call will occur within the next minute. Find the probability that less than 20 calls occur within an hour. View keyboard shortcuts EditViewInsertFormatToolsTable 12pt Paragraph
- The lifetime (in days) of a certain electronic component that operates in a high-temperature environment is lognormally distributed with μ = 1.9 and σ = 0.4. Find the probability that a component lasts between three and six days.The operator of a pumping station has observed that demand for water during early afternoon hours has an approximately exponential distribution with mean 1000 cfs (cubic feet per second). b) What water-pumping capacity should the station maintain during early afternoons so that the probability that demand will be below the capacity on a randomly selected day is 0.995? c) Of the three randomly selected afternoons, what is the probability that on at least two afternoons the demand will exceed 700 cfs?A manufacturer claims that the tensile strength of a certain composite (in MPa) has the lognormal distribution with μ = 5 and σ = 0.5. Let X be the strength of a randomly sampled specimen of this composite. a) If the claim is true, what is P(X < 20)? b) Based on the answer to part (a), if the claim is true, would a strength of 20 MPa be unusually small? c) If you observed a tensile strength of 20 MPa, would this be convincing evidence that the claim is false? Explain. d) If the claim is true, what is P(X < 130)? e) Based on the answer to part (d), if the claim is true, would a strength of 130 MPa be unusually small? f) If you observed a tensile strength of 130 MPa, would this be convincing evidence that the claim is false? Explain.
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