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A firm produces 2 different alarm systems A and B. System A detects with
probability 0.93 and costs 2 times expensive then system B. System B detects
fire with probability 0.8. Which option is better: to set two systems B or one
system A?
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- 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?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?7. Assume that there is a 9% rate of disk drive failure in a year. a. If all your computer data is stored on a hard disk drive with a copy stored on a second hard disk drive, what is the probability that during a year, you can avoid catastrophe with at least one working drive? b. If copies of all your computer data are stored on three independent hard disk drives, what is the probability that during a year, you can avoid catastrophe with at least one working drive? a. With two hard disk drives, the probability that catastrophe can be avoided is nothing. (Round to four decimal places as needed.)
- A company installs new central-heating furnaces and has found that for 15% of all installations, a return visit is needed to make some modifications. Six installations were made in a particular week. Assume independence of outcomes for these installations.a. What is the probability that a return visit will be needed in all these cases?b. What is the probability that a return visit will be needed in none of these cases?c. What is the probability that a return visit will be needed in more than 1 of these cases?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?Deborah Holwager, a concessionaire for the Amway Center in Orlando, has developed a table of conditional values for the various alternatives (stocking decision) and states of nature (size of crowd) Alternatives States of Nature (size of crowd) Large Average Small Large Inventory Ave yge Inventory Smal Inventory $12,000 -51,000 $18,000 $15.000 $16,000 $4,000 $10,000 $5,000 Probabilities associated with the states of nature are 0.35 for a large crowd, 0.50 for an average crowd, and 0.15 for a small crowd. $6.000 a) The alternative that provides Deborah the greatest oxpected monetary value (EMV) is The EMV for this decision is s (enter your answer as a whole number).
- e) (P1, P2, P3, y1, y2, y3) = (0, 77, 109, 0, 1, 1) with a profit of $ 5260is wrong28. An expensive piece of equipment is used in the masking operation for semi- conductor manufacture. A capacitor in the equipment fails randomly. The capacitor costs $7.50, but if it burns out while the machine is in use, the production process must be halted. Here the replacement cost is estimated to be $150. Based on past experience, the lifetime distribution of the capacitor is estimated to be Probability of Failure Number of Months of Service 1 .08 2 .12 3 .16 4 .26 5 .22 .16 How often should the capacitors be replaced in order to minimize the expected monthly cost of planned and unplanned replacement?1. What is the most the real estate investor would be willing to pay for additional information? Use Minimum Expected Regret (Minimum EOL) 2. Use the alternative method to verify EVPI
- 9.19 In bottle production, bubbles that appear in the glass are considered defects. Any botle that has more than two bubbles is elassified as "nonconforming" and is sent to recycling Suppose that a particular production line produces bottles with bubbles at a rate of 1. bubbles per bottle. Bubbles occur independently of one another. a What is the probability that a randomly chosen bottle is nonconfornming? b Bottles are packed in cases of 12. An inspector chooses one bottle from each case and examines it for defects. If it is nonconforming, she inspects the entire case, re placing nonconforming bottles with good ones. This process is called rectification If the chosen bottle conforms (has two or fewer bubbles), then she passes the cuse. In total, 20 cases are produced. What is the probability that at least 18 of them pass! c What is the expected number of nonconforming bottles in the 20 cases after they have been inspected and rectified using the scheme described in part b?17- According to a business plan for a startup, the break-even point was calculated at 12,000 units of sales. However, after launch, the average variable cost for the product has gone up. Which of the following is the effect on break-even point? Group of answer choices the effect on break-even point cannot be determined without more information the break-even point will remain the same the break-even point will be higher than 12,000 units the break-even point will be lower than 12,000 units 18- According to a business plan for a startup, the break-even point was calculated at 12,000 units of sales. However, after launch, the unit price for the product had to be lowered. Which of the following is the effect on break-even point? Group of answer choices the break-even point will remain the same the break-even point will be lower than 12,000 units the effect on break-even point cannot be determined without more information the break-even point will be higher than 12,000…11. Select a fusible disconnect and the fuses for the application below. CNC Grinding Station Machine Operating Voltage - 600 VAC, 3-phase Spindle Motor FLA = 25 Amps Table Motor FLA = 10 Amps Fusible Disconnect Voltage Rating Fusible Disconnect Current Rating Number of Poles Fuse Voltage Rating Fuse Current Rating (VAC) (Amps) (VAC) (Amps)