12) Thirty six percent of all assembly line mechanical robots are claimed for services by the technicians to be sent out to the manufacturer all under the issued warranty at the time of purchase. Out of these robots sent under warranty, 45% will be repaired and sent back to the factory and 55% will be replaced under warranty at no cost. Suppose the company you are working for recently ordered 15 of these mechanical robots. The CEO agreed to sign a five years purchasing contract if only the probability of sending back three of these robots are LESS than 0.24 during the life of the contract. Will she approve the purchasing contact? [Hint: you are trying to find the probability of exactly three robots will eventually be replaced under warranty as she will not sign off if such probability for three is more than 24%.]

12) Thirty six percent of all assembly line mechanical robots are claimed for services by the technicians to be sent out to the manufacturer all under the issued warranty at the time of purchase. Out of these robots sent under warranty, 45% will be repaired and sent back to the factory and 55% will be replaced under warranty at no cost. Suppose the company you are working for recently ordered 15 of these mechanical robots. The CEO agreed to sign a five years purchasing contract if only the probability of sending back three of these robots are LESS than 0.24 during the life of the contract. Will she approve the purchasing contact? [Hint: you are trying to find the probability of exactly three robots will eventually be replaced under warranty as she will not sign off if such probability for three is more than 24%.]

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Description: 12) Thirty six percent of all assembly line mechanical robots are claimed for services by the technicians to besent out to the manufacturer all under the issued warranty at the time of purchase. Out of these robots sentunder warranty, 45% will be re

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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2. A research Development department at Oda manufacturing company determines that 20% of people who purchase their products during any given month will not purchase the next month. On the other hand, 30% of the people who could not purchase during any given month will purchase in the next month. On a population of 1000 people 100 purchased their products this month. How many will purchase their product. 1. In the long run?
2. A research Development department at Oda manufacturing company determines that 20% of people who purchase their products during any given month will not purchase the next month. On the other hand, 30% of the people-who could not purchase during any given month will purchase in the next month. On a population of 1000 people 100 purchased their products this month. How many will purchase their product. A. In the long run?
Suppose that a sales force has found 15 qualified buyers and has begun the sales process. The sales manager estimates that 10% eventually proceeds to make a purchase. Assume that a professional company offers three services, priced at P7,000, P10,000 and P14,000, respectively. Based on past results or the sales manager’s estimates, you project that 60% of first-time buyers will choose the cheapest option, 30% will choose the middle option and 10% will choose the most expensive option. a. Calculate the size of a likely sale for any prospect that makes a purchase. b. How many qualified buyers must be found in order for the company to generate P80, 000 in sales in a given period?
The chief loan officer of La Crosse Home Mortgage Company summarized the housing loans extended by the company in 2017 according to type and term of the loan. Her list shows that 60% of the loans were fixed-rate mortgages (F), 30%were adjustable-rate mortgages (A), and 10% belong to some other category (O) (mostly second trust-deed loans and home equity loans). Of the fixed-rate mortgages, 75% were 30-year loans and 25% were 15-year loans; of the adjustable-rate mortgages, 30% were 30-year loans and 70% were 15-year loans; finally, of the other loans extended, 25% were 20-year loans, 60% were 10-year loans, and 15% were for a term of 5 years or less. What is the probability that a home loan extended by La Crosse has an adjustable rate and is for a term of 15 years? What is the probability that a home loan extended by La Crosse is for a term of 15 years?
Based on Lanzenauer et al. (1987). To process income tax forms, the IRS first sends each form through the data preparation (DP) department, where information is coded for computer entry. Then the form is sent to data entry (DE), where it is entered into the computer. During the next 3 weeks, the following quantities of forms will arrive: week 1, 40,000; week 2, 30,000; and week 3, 60,000. All employees work 40 hours per week and are paid $500 per week. Data preparation of a form requires 15 minutes, and data entry of a form requires 10 minutes. Each week, an employee is assigned to either data entry or data preparation. The IRS must complete processing all forms by the end of week 5 and wants to minimize the cost of accomplishing this goal. Assume that all workers are full-time employees and that the IRS will have the same number of employees each week. Assume that all employees are capable of performing data preparation and data entry. Determine how many workers should be working and…
Consider two companies with mining rights to the same region. They couldmine in an environmentally friendly manner or agressively. If both mineenvironmentally friendly, profits are 100 million for each in a given year.If they both mine agressively, the government will step in and fine them,meaning that they will make 75 million each. Finally, the government willnot step in if only one of the companies mines agressively, meaning that theaggresive miner will make 120 million while the environmentally friendlyminer will loose out in capacity and make 50 million.a) Write the normal form of the game and point out the Nash equilibriumif the game is played only once. (2)b) What will be the rollback equilibrium if the two companies mine thesame region three years ina row? (2)c) Now assume that the game is repeated infinitely. What rate of returnvalue that will sustain the environmentally friendly strategy as the Nashequilibrium if one of the companies is playing a grim strategy? (3)d) Now…
The government of Antigua wishes to introduce income tax to increase government revenue. In so doing, a consultant was hired to make recommendations on the best way forward. The consultant proposed that the government shouldn’t tax any employee earning below XCD25,000.00 annually or the employee first XCD25,000.00 annually. Thereafter, any employee earning between XCD25,000.00 and XCD40,000.00 annually should pay 5.5% income tax and then any employee earning above XCD40,000.00 should pay 10.5% income tax. For the above information: a) Derive a mathematical function to represent the consultant’s position clearly identifying all variables and intervals. b) From part a) above, state the name of ALL the mathematical functions derived. c) If Jane (someone working in Antigua) pays XCD750.00 in income tax, calculate Jane’s annual income.
The government of Antigua wishes to introduce income tax to increase government revenue. In so doing, a consultant was hired to make recommendations on the best way forward. The consultant proposed that the government shouldn’t tax any employee earning below XCD25,000.00 annually or the employee first XCD25,000.00 annually. Thereafter, any employee earning between XCD25,000.00 and XCD40,000.00 annually should pay 5.5% income tax and then any employee earning above XCD40,000.00 should pay 10.5% income tax. For the above information Derive a mathematical function to represent the consultant’s position clearly identifying all variables and intervals. From part a) above, state the name of ALL the mathematical functions derived. If Jane (someone working in Antigua) pays XCD750.00 in income tax, calculate Jane’s annual…
The government of Antigua wishes to introduce income tax to increase government revenue. In so doing, a consultant was hired to make recommendations on the best way forward. The consultant proposed that the government shouldn’t tax any employee earning below XCD25,000.00 annually or the employee first XCD25,000.00 annually. Thereafter, any employee earning between XCD25,000.00 and XCD40,000.00 annually should pay 5.5% income tax and then any employee earning above XCD40,000.00 should pay 10.5% income tax. For the above information Derive a mathematical function to represent the consultant’s position clearly identifying all variables and intervals. From part a) above, state the name of ALL the mathematical functions derived.
Suppose the post office had 25 full-time employees andwas not allowed to hire or fire any employees. Formulate anLP that could be used to schedule the employees in order tomaximize the number of weekend days off received by theemployees.
Suppose that a healthy person has 10% chance of getting sick that would require $40,000 of medical expenses. Suppose that unhealthy person has a 60% chance of getting sick that would require $100,000 in medical expenses. A) What would be an actuarially fair premium for a healthy person? B) What would be an actuarially fair premium for unhealthy person? C) If everyone has to buy health insurance and 20% of the population are unhealthy and 80% of the population are health, what would be an actuarially fair premium for any person?
Suppose that for a recent admissions class, an Ivy League college received 2,825 applications for early admission. Of this group, it admitted 1,007 students early, rejected 854 outright, and deferred 964 to the regular admission pool for further consideration. In the past, this school has admitted 18% of the deferred early admission applicants during the regular admission process. Counting the students admitted early and the students admitted during the regular admission process, the total class size was 2,375. Let E, R, and D represent the events that a student who applies for early admission is admitted early, rejected outright, or deferred to the regular admissions pool. (a) Use the data to estimate P(E ), P(R), and P(D). If required, round your answers to four decimal places. P(E) = P(R) = P(D) = (b) Are events E and D mutually exclusive? Find P(E ∩ D). If your answer is zero, enter "0". (c) For the 2,375 students who were…