2₁ a. A product consists of three subassemblies which are connected in series. The first subassembly consists of components A and B, which are connected in parallel. In the second subassembly, components C and D are connected in series. The third subassembly has only component E. The reliabilities of the components are given in the following table. Component D A C E B Reliability 0.92 0.95 0.98 0.92 0.96 Find the reliability of the product.
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- The injured football player Bad news everyone! There is 1 second left in the game, and Tom Brady has injured himself. The matrices below depict the relative probabilities of winning givenan offensive and a defensive play call. (The row player is the New England Patriots and the column player is the opponent.) How much has the all star's home team probability of winning decreased due to the injury? Pass uny Patriots D Pass .4, .6 D Run .9,.1 .8,.2 .5,.5 Pass Run Opponent D Pass D Run .06, .94 .32, .68 .8,.2 .5,.5Suppose A and B are two events with probabilities: P(A) = .30, P(B°) = .45, P(AN B) = .15. Find the following: а) Р(A U B). b) Р (4°). с) Р(B).The owner of Tastee Cookies needs to decide whether to lease a small, medium, or large new retail outlet. She estimates that monthly profits will vary with demand for her cookies as follows: SIZE OFOUTLET DEMAND LOW HIGH Small $ 1,000 1,000 Medium 500 2,500 Large 0 3,000 For what range of probability that demand will be high, will she decide to lease the medium facility?
- 21. The amount of bread (in hundreds of pounds) x that a certain bakery is able to sell in a day is found to be a numerical valued random phenomenon, with a probabiliiy function specified by the p.d.f. f(x), given by : k. x ={k. (10 – x), for 5a. A company produces lightbulbs whose life follows a normal distribution, with mean 1200 hours and standard deviation 250 hours. If we choose a lightbulb at random, what is the probability that its lifetime will be between 900 and 1300 hours? (answer in three decimal places)Explain probability and nonprobability samplingtechniques.Managers of the restaurant, NicePizzeria@Nola, have to plan for the number of pizzas they want to make at the beginning of each day. Based on market research, the managers know the daily demand can only be one of the three levels: 30, 40 or 50 pizzas. Also, the probabilities of getting a daily demand of 30, 40, 50 pizzas are 0.3, 0.4, 0.3 respectively. The managers decide that their tentative daily supply of pizza should also be one of the three levels: 30, 40 or 50 pizzas. Each pizza costs $3 to make and the price is $8 per pizza. Note: The profit for each pizza sold is $5. For the ones supplied but not sold, the profit is -$3. Fill in the following profit table (hint: use two-way table ) and use the profit table to answer the questions. Three demand levels 30 40 50 30 Three supply 40 levels 50 1) What is the maximin supply level? 2) What is the maximum expected profit (across three supply levels)?The probability that a visitor to an animal shelter will adopt a dog is 0.10. Out of 9 visits, what is the probability that at least (equal to or more than) 1 dog will be adopted? a. 0.3874 b. 0.6126 c. 0.5639 d. 0.1342Airline passengers arrive randomly and independently at the passenger-screening facility at a major international airport. The mean arrival rate is 11 passengers per minute. a. Compute the probability of no arrivals in a one-minute period (to 6 decimals). b. Compute the probability that three or fewer passengers arrive in a one-minute period (to 4 decimals). c. Compute the probability of no arrivals in a 15-second period (to 4 decimals). d. Compute the probability of at least one arrival in a 15-second period (to 4 decimals).Players would draw a card from a standard 52 card deck. Whatever card they drew determined what they won. If they draw a face card (Jack, King, Queen) then they win $5. If they draw an Ace, they win $15. For all other cards, they win nothing. A. Fill out the probability distribution table with the probabilities of each possible outcome for this game. Round decimals to four places. x $15 $5 $0 P(x) B. What is the expected value of the distribution above? (Round to the nearest cent, two decimal places.) C. If players were charged $2 per game, would they make and average profit on the games over time, or would they take an average loss over time? D. If players were charged $3 per game, would they make and average profit on the games over time, or would they take an average loss over time?Suppose that a car - rental agency offers insurance for a week that costs $125. A minor fender bender will cost 34000 whereas a major accident might cost $16 comma 000 in repairs. Without the insurance, you would be personally liable for any damages. There are two decision alternatives: take the insurance, or do not take the insurance. You researched insurance industry statistics and found out that the probability of a major accident is 0.04% and that the probability of a fender bender is 0.18%. The expected payoff if you buy the insurance is $125.00. The expected payoff if you do not buy the insurance is $12.52. Develop a utility function for the payoffs associated with this decision for a risk-averse person. Determine the decision that would result using the utilities instead of the payoffs. Based on the expected payoffs, the best decision is to not purchase the insurance. Are these two decisions consistent?The promoter of a football game is concerned that it will rain. She has the option of spending $14,040 on insurance that will pay $39,000 if it rains. She estimates that the revenue from the game will be $65,040 if it does not rain and $30,040 if it does rain. What must the chance of rain be if buying the policy has the same expected return as not buying it? Write expressions showing the expected returns if the promoter does and does not purchase the insurance, using p to represent the probability of rain. Without insurance, E(return) = With insurance, E(return) = The chance of rain must be _%.SEE MORE QUESTIONS