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.
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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.
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- An electronic chess 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 at least 45 months b) The probability that any given unit will fail sooner than 30 monthsA major television manufacturer has determined that its 40-inch LED televisions have a meanservice life that can be modeled by a normal distribution with a mean of six years and a standarddeviation of one-half year.a. What probability can you assign to service lives of at least (1) five years? (2) six years? (3)seven and one-half years?Consider the following system: → 0.90 → 0. 90 → Determine the probability that the system will operate under each of these conditions: a. The system as shown. (Do not round your intermediate calculations. Round your final answer to 4 decimal places.) b. Each system component has a backup with a probability of 0.90 and a switch that is 100 percent reliable. (Do not round your intermediate calculations. Round your final answer to 4 decimal places.) c. Each system component has a backup with a probability of 0.90 and a switch that is 99 percent reliable. (Do not round your intermediate calculations. Round your final answer to 4 decimal places.)
- A product engineer has developed the following equation for the cost of a system component: C = (10P)2, where is the cost in dollars and Pis the probability that the component will operate as expected. The system is composed of two identical components, both of which must operate for the system to operate. The engineer can spend $173 for the two components. To the nearest two decimal places, what is the largest component probability that can be achieved?A local military base maintains a variety of different equipment. One of these is a sensitive radardevice that signals incursion of enemy planes into American airspace. Breakdowns of the device occur completely at random at an average rate of three per year. The equipment is generally repaired the same day that it fails. Determine the following:b. The probability that there are exactly five breakdowns in any given year.A product engineer has developed the following equation for the cost of a system component: C = (10P)2, where C is the cost in dollars and P is the probability that the component will operate as expected. The system is composed of 3 identical components, all of which must operate for the system to operate. The engineer can spend $254 for the 3 components. What is the largest component probability that can be achieved? (Do not round your intermediate calculations. Round your final answer to 4 decimal places.) Probability 0.8466
- A product engineer has developed the following equation for the cost of a system component: C = (10P) 2, where C is the cost in dollars and P is the probability that the component will operate as expected. The system is composed of two identical components, both of which must operate forthe system to operate. The engineer can spend $173 for the two components. To the nearest two decimal places, what is the largest component probability that can be achieved?A product is composed of four parts. In order for the product to function properly in a given situation, each of the parts must function. Two of the parts have a 0.96 probability of functioning, and two have a probability of 0.99. (Leave your answers in 4 decimal places).A hospital has three independent fire alarm systems, with reliabilities of .95, .97, and .99. In the event of a fire, what is the probability that a warning would be given?
- A production process contains a machine that deteriorates rapidly in both quality and output under heavy usage, so that it is inspected at the end of each day. Immediately after inspection, the condition of the machine is noted and classified into one of the four possible states: State Condition Good as new Operable-minimum deterioration Operable-major deterioration Inoperable 2 3 The process can be modeled as a Markov Chain with its (one-step) transition matrix P given by 1 7 1 - 16 8 16 3 1 1 P = 8. 4 8. 1 1 2 a. Determine the expected life of a new machine if it is replaced when it is "Inoperable". b. Determine the expected life of a new machine if it is replaced when it is either "Operable-major deterioration" or "Inoperable". c. According to the replacement rule in b., what is the percentage of machines that are replaced when they are inoperable?A local cab company maintains a fleet of 10 cabs. Each time a cab breaks down, it isrepaired the same day. Assume that breakdowns of individual cabs occur completely atrandom at a rate of two per year.d. What is the probability that there are more than five breakdowns between Thanksgiving Day (November 28) and New Year’s Day (January 1)?7. A piece of equipment has a lifetime T (measured in years) that is a continuous ran- dom variable with cumulative distribution function F(t) = 1 – e/10 – (1/10) e¯/10 for all t> 0. a. What is the probability density function of T? b. What is the probability that a piece of equipment survives more than 20 years? c. What is the probability that a piece of equipment survives more than 10 years but fewer than 20 years? d. What is the probability that a piece of equipment survives more than 20 years given that it has survived for 10 years? 8. For the equipment mentioned in Problem 7, a. Derive the failure rate function r(1), and draw a graph of the function. b. Without using the failure rate function, determine the probability that a piece of equipment that has survived 20 years of operation fails in the 21st year. c. Does r(20) accurately estimate your answer to part (b)? Why or why not?