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)?e. For what reason might your answer in part (d) be too low?
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A local cab company maintains a fleet of 10 cabs. Each time a cab breaks down, it is
repaired the same day. Assume that breakdowns of individual cabs occur completely at
random 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)?
e. For what reason might your answer in part (d) be too low?
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- 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)?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.a. What is the probability that any particular cab will run for a full year withoutsuffering a breakdown?Jankord Jewelers permits the return of their diamond wedding rings, provided the return occurs within two weeks. Typically, 20 percent are returned. If nine rings are sold today, what is the probability that fewer than four will be returned? A- 0.914 B- 0.962 C- 0.923 D- 0.935
- Six thousand light bulbs light a large hotel and casino marquee. Each bulb fails completely at random, and each has an average lifetime of 3,280 hours. Assuming that the marquee stays lit continuously and bulbs that burn out are replaced immediately, how many replacements must be made each year on the average?A collection of 30 Christmas tree lights are arranged in a pure series circuit; that is, ifone of the lights burns out, then the entire string goes out. Suppose that each light failscompletely at random at a rate of one failure every year. What is the probability that thelights will burn from the beginning of Christmas Eve (December 24) to the end of NewYear’s Day (January 1) without failure?Wizard, a popular brand of electric garage door opener, includes two 40-watt bulbs that go onwhen the garage door is opened. A bulb will generally last about one year in normal operation.Three neighbors, James, Smith, and Walker, each has a Wizard opener in their respectivegarages. Each time a bulb burns out, James replaces both bulbs. Smith, on the other hand, replaces only the bulb that has burned out, and Walker replaces both bulbs only after both haveburned out. Assume that light bulbs fail according to an exponential law.b. What percentage of the time will Walker have only one bulb burning?
- Wizard, a popular brand of electric garage door opener, includes two 40-watt bulbs that go onwhen the garage door is opened. A bulb will generally last about one year in normal operation.Three neighbors, James, Smith, and Walker, each has a Wizard opener in their respectivegarages. Each time a bulb burns out, James replaces both bulbs. Smith, on the other hand, replaces only the bulb that has burned out, and Walker replaces both bulbs only after both haveburned out. Assume that light bulbs fail according to an exponential law.c. Is there any advantage of James’s strategy over Smith’s?Wizard, a popular brand of electric garage door opener, includes two 40-watt bulbs that go onwhen the garage door is opened. A bulb will generally last about one year in normal operation.Three neighbors, James, Smith, and Walker, each has a Wizard opener in their respectivegarages. Each time a bulb burns out, James replaces both bulbs. Smith, on the other hand, replaces only the bulb that has burned out, and Walker replaces both bulbs only after both haveburned out. Assume that light bulbs fail according to an exponential law.a. Over a 10-year period, how many bulbs, on average, will each neighbor require?The length of time between breakdowns of an essential piece of equipment is important in the decision of the use of auxiliary equipment. An engineer thinks that the best “model” for time between breakdowns of a generator is the exponential distribution with a mean of 15 days. If the generator has just broken down, what is the probability that it will break down in the next 12 to 24 days?
- The assumption that a system will operate in a stable environment without risk is not realistic (Sales et al., 2018). Risk is widely classified into disruption and operational risks (Kleindorfer & Saad, 2005; Tang, 2006). Extreme uncertainty and the absence of synchronization between supply and demand are linked to operational risks while circumstances such as labor strikes, terrorist attacks, and natural calamities are related to disruption risks (Lockamy & McCormack, 2010). The probability of human injury or even death is high in disruptions such as multi-casualty disasters which brings about the challenge of increased pressure on healthcare. Healthcare institutions are required to become capable of understanding and adapting to environmental changes to mitigate such unexpected changes. These unexpected changes can affect the competitiveness, responsiveness and operating procedures of a firm significantly (Huang, Yen, & Liu, 2014), and for healthcare institutions, the…A wheel tractor-scraper is carrying a 50,000 lb load while operating on a level grade. Assume no power derating is required for equipment condition, altitude, and temperature. What minimum value of coefficient of traction between the tractor wheels and the traveling surface is needed to overcome an equivalent rolling resistance of 12%? For the fully loaded condition 40% of the weight is distributed to the drive axle. Operating weight of the scraper when empty is 70,000 lb.6.4 (5 pts) A wheel tractor-scraper is carrying a 50,000 lb load while operating on a level grade. Assume no power derating is required for equipment condition, altitude, and temperature. What minimum value of coefficient of traction between the tractor wheels and the traveling surface is needed to overcome an equivalent rolling resistance of 12%? For the fully loaded condition 40% of the weight is distributed to the drive axle. Operating weight of the scraper when empty is 70,000 lb.Consider a product that is "settled in." Its MTBF distribution has been found to be normal with a mean of 10,000 hours and a standard deviation of 100 hours. Answer the following questions: (a) Calculate the probability of a breakdown before 8,000 hours? (b) Calculate the probability of a breakdown before 9,000 hours? (c) Would you prefer a policy of “preventive maintenance” or a policy of “breakdown maintenance” on this product? Explain your choice.