Concept explainers
a
Interpretation:
Probability Density Function
Concept Introduction:
Probability Distribution Function is a likelihood of an event to occur for discrete random variables. Graphically, it shows how likely variables will fall under the probability area.
b
Interpretation:
Probability that a piece of equipment survives more than 20 years.
Probability is the likelihood of an event to occur.. It ranges between 0 to 1. O implies no chance of occurance while 1 implies 100% chance of occurance.
c
Interpretation:
Probability that a piece of equipment survives more than 10 years but fewer than 20 years.
Concept Introduction:
Exponential distribution is a probabilitydistribution which finds probability of an event to occur between independent constant rate and continous rate.
Probability is the likelihood of an event to occur.. It ranges between 0 to 1. O implies no chance of occurance while 1 implies 100% chance of occurance.
d
Interpretation:
Probability that a piece of equipment survives more than 20 years given it has survived for 10 years
Concept Introduction:
Exponential distribution is a probabilitydistribution which finds probability of an event to occur between independent constant rate and continous rate.
Probability is the likelihood of an event to occur.. It ranges between 0 to 1. O implies no chance of occurance while 1 implies 100% chance of occurance.
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EBK PRODUCTION AND OPERATIONS ANALYSIS
- The game of Chuck-a-Luck is played as follows: You pick a number between 1 and 6 and toss three dice. If your number does not appear, you lose 1. If your number appears x times, you win x. On the average, use simulation to find the average amount of money you will win or lose on each play of the game.arrow_forwardIf a student attends every business analytics class, the probability of passing the course is 0.90; but if the student only attends randomly, then the probability of passing the course is 0.30. If a student fails, he or she can take a makeup exam where the probability of passing is 0.60 if the student has attended every class. This probability of passing the makeup exam drops to 0.20 if the student has attended at random. Passing the course is worth 5 credits. Full-time attendance "costs" 3 credits in terms of energy and time, whereas random attendance "costs" only 1 credit. Draw a decision tree and use the decision tree to decide which is the best attendance pattern to adopt. Assume that all failing students take the makeup exam and that the payoff for failing is equal to 0 credit. Draw a decision tree and determine the payoff for each decision and event node. Which alternative should the student choose?arrow_forwardFill in the P(X=x) values to give a legitimate probability distribution for the discrete random variable X, whose possible values are -3, 0, 4, 5, and 6. Value x of X P (X = x) -3 0 0.23 5 0.17 6 0.30arrow_forward
- An expensive piece of equipment is used in the masking operation for semiconductor 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 Number of Months Probability of of Service Failure 1 .08 2 .12 3 .16 4 .26 5 .22 6…arrow_forwardWhich of the following gambles has the largest objective risk? 20% chance of winning $100 and 80% chance of losing $100 50% chance of winning $10,000 and 50% chance of losing $10,000 50% chance of winning nothing and 50% chance of losing $100 50% chance of winning $100 and 50% chance of winning nothingarrow_forwardIn designing a new space vehicle, NASA needs to decide whether to provide 0, 1 or 2 backup systems for a critical component of the vehicle. The first backup system, if included, comes into use only if the original system fails. The second backup system, if included, comes into use only if the original system and the first backup system both fail. NASA engineers claim that each system, independent of the others, has a 1.5% chance of failing if called into use. Each backup system costs $70,000 to produce and install within the vehicle. Once the vehicle is in flight, the mission will be scrubbed (ended early) only if the original system and all backups fail. The cost of a scrubbed mission, in addition to production costs, is assessed to be $5,000,000. How many backup systems are needed to minimize NASA’s expected total cost?arrow_forward
- A NY Times best-selling author wants to write a new book as either volume II of her earlier successful book or an autobiography. She believes that by writing the volume II, given her previous success, she will have a 50% chance of placing it with a major publisher where it should ultimately sell about 40,000 copies. However, the worst-case scenario, if she can’t get a major publisher to take it, then she thinks there is 80% chance of placing it with a smaller publisher, with sales of 30,000 copies. On the other hand, if she writes an autobiography, considering the potential interest in her journey as successful writer, she thinks there will be 40% chance of placing it with a major publisher, and it should result in ultimate sales of about 50,000 copies. If she can’t get a major publisher to take it, the worst-case scenario, she thinks there is a 50% chance of placing it with a smaller publisher, with ultimate sales of 35,000 copies. Construct a decision tree to help this author…arrow_forwardTo a health insurance company, the total claims (payout) expected for a group of insured persons depend on all of the following except a)the number of insured persons in the group. b)the average income of persons in the group. c)the average cost of an illness. d)the probability of illness for the insured persons.arrow_forwardA recent 10-year study conducted by a research team at the Great Falls Medical School was conducted to assess how age, systolic blood pressure, and smoking relate to the risk of strokes. Assume that the following data are from a portion of this study. Risk is interpreted as the probability (times 100) that the patient will have a stroke over the next 10-year period. For the smoking variable, define a dummy variable with 1 indicating a smoker and 0 indicating a nonsmoker. The data is provided below: Risk of Strokes Age Systolic Blood Pressure Smoker 10 59 156 0 25 65 163 0 12 60 158 0 57 86 177 1 28 59 196 0 50 76 189 1 17 57 159 1 34 78 120 1 37 80 135 1 15 78 98 0 22 71 152 1 39 70 173 1 17 67 135 0 48 77 209 1 18 60 199 0 36 82 119 1 10 66 166 0 34 80 125 1 4 62 117 0 38 59…arrow_forward
- A television network earns an average of $25 million each season from a hit program and loses an average of $8 million each season on a program that turns out to be a flop. Of all programs picked up by this network in recent years, 25% turn out to be hits and 75% turn out to be flops. At a cost of C dollars, a market research firm will analyze a pilot episode of a prospec- tive program and issue a report predicting whether the given programwill end up being a hit. If the program is actually going to be a hit, there is a 75% chance that the market researchers will predict the program to be a hit. If the program is actually going to be a flop, there is only a 30% chance that the market researchers will predict the program to be a hit.a. What is the maximum value of C that the network should be willing to pay the market research firm?b. Calculate and interpret EVPI for this decision problem.arrow_forwardUsing @risk draw a normal distribution with a mean of 500 and a sd of 100. What is the probability the random number is less than 450arrow_forwardTexas Petroleum Company is a producer of crude oil that is considering two drilling projects with the following profit outcomes and associated probabilities: Drilling Project, A Profit -$300,000 100,000 500,000 600,000 Probability (percent) 10 60 20 10 Drilling Project, B Profit -$600,000 100,000 300,000 1,000,000 The manager's attitude toward risk is as follows: Profit ($'000) -600 -300 100 U(II) 0.00 0.05 0.20 Note: U(II) stands for utility index of profit. 300 0.30 500 0.45 Probability (percent) 15 25 40 20 600 0.55 1,000 1.00 In making decision under risk, which project will be chosen by the manager of Texas Petroleum Company based on his behaviour toward risk? Also describe the manager's ways of handling decision-making associate with risk. Justify your answers using numerical explanation.arrow_forward
- Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,