Theorem is a mathematical representation that helps one to calculate conditional probability. It relates inverse representation of the probabilities concerning two events. This theorem is named after the British Mathematician Thomas Bayes. It is represented by P(A‚ B)= P(A B) P(B) or P (A‚ B)=P(B A)P(A) So P(A|B)P(B) = P(B|A)P(A) The Law of Total Probability: P(B) = P(B/A).P(A) + P(B/A′) . P(A′) Total probability and multiplication rule: P(A/B) = P(B/A).P(A) (multiplication
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Problems (f) This assignment is a sampling of question types. Preparation for Test #2 should include all questions provided to you (i.e. class examples‚ Practice Problems‚ Practice Test and this assignment). (g) Remember that Test#2 will include (1) Probability material‚ including (2) Binomial Distribution and (3) one Calculus question. Questions: 1. The following table gives the results of a survey of 900 movie goers in a particular city‚ their gender‚ age and preference for film-genre. Age (years)
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574 for the ‘Order 10‚000 shirts’ decision. It should be noted that while there was an equal likelihood of 80‚000 and 20‚000 grandstand seats‚ George felt that there was a very slightly higher probability of 80‚000 seats for this concert. This intuition has been reflected in the tree diagram with probabilities for the higher extreme and lower extreme as 30% and
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distribution of the sample mean? b. What is the probability that these 64 students will spend a combined total of more than $715.21? c. What is the probability that these 64 students will spend a combined total between $703.59 and $728.45? ANS: a. 10.5 0.363 normal b. 0.0314 c. 0.0794 2. The life expectancy in the United States is 75 with a standard deviation of 7 years. A random sample of 49 individuals is selected. a. What is the probability that the sample mean will be larger than
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PROBABILITY AND STATISTICS Lab‚ Seminar‚ Lecture 4. Behavior of the sample average X-bar The topic of 4th seminar&lab is the average of the population that has a certain characteristic. This average is the population parameter of interest‚ denoted by the greek letter mu. We estimate this parameter with the statistic x-bar‚ the average in the sample. Probability and statistics - Karol Flisikowski X-bar Definition 1 x xi n i 1 Probability and statistics - Karol Flisikowski
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Estimate the indicated probability. 1) The table shows the number of college students who prefer a given pizza topping. toppings freshman sophomore cheese 14 16 meat 19 26 veggie 16 14 junior 20 16 19 senior 26 14 26 1) Determine the empirical probability that a student prefers cheese toppings. Find the probability. 2) A bag contains 2 red marbles‚ 4 blue marbles‚ and 8 green marbles. What is the probability of choosing a blue marble? 2) 3) Determine the probability that the spinner lands
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packages were underweight and some were overweight‚ but most of them had satisfactory weight. What is the probability of selecting three packages that are satisfactory? Answer: P(all 3 satisfactory) = (0.9) (0.9) (0.9) = 0.729 2) A study of interior designers ’ opinions with respect to the most desirable primary color for executive offices showed that: What is the probability that a designer does not prefer blue? Answer: Total is 400. So‚ P(prefer Blue) = 37/400 = 0.0925
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Assignment Week 1 Answer the following questions: 1. Describe the rationale for utilizing probability concepts. For practical reasons‚ variables are observed to collect data. The sampled data is then analyzed to elicit information for decision making in business and indeed in all human endeavors. However‚ sampled information is incomplete and not free from sampling error. Its use in decision-making processes introduces an element of chance. Therefore‚ it is important for a decision-maker
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Curriculum Framework Lisa Hammond Southern New Hampshire University Curriculum Framework The task of building a curriculum that shows what is important for students to be able to demonstrate has many facets that need to be analyzed. The development of curriculum is an on-going assignment of a teacher ’s responsibilities. If a teacher is taking good notes and observing
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four entries each. One could say that an n-node network uses n different kinds of pheromones. The entries in the tables are the probabilities which influence the ants’ selection of the next node on the way to their destination node. Figure 4 shows a possible network configuration and a pheromone table. For example‚ ants travelling from node 1 to node 3 have a 0.49 probability of choosing node 2 as their next node‚ and 0.51 of choosing node
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