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The document discusses the mean, variance, and standard deviation of binomial distributions. It provides examples of calculating these values for randomly guessing answers on a multiple choice test and polling voters in an election where preferences are assumed to be evenly split. It explains how to use the calculated standard deviation to determine if outcomes are unusual or within the expected range.
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The document discusses key concepts related to the binomial distribution including:
- How to calculate the mean, variance, and standard deviation of a binomial distribution
- An example of calculating these values for randomly guessing answers on a 100 question multiple choice test
- How the mean and standard deviation can be used to determine what outcomes would be considered usual or unexpected
- Two additional examples applying these concepts to polling data about candidate preferences
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The document discusses the mean, variance, and standard deviation of binomial distributions. It provides examples of calculating these values for randomly guessing answers on a multiple choice test and polling voters with a presumed even split between two candidates. It concludes with homework problems involving binomial distributions.
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The document discusses key concepts related to the binomial distribution including:
- How to calculate the mean, variance, and standard deviation of a binomial distribution
- An example of calculating these values for randomly guessing answers on a 100 question multiple choice test
- How the mean and standard deviation can be used to determine what outcomes would be considered usual or unexpected
- Two additional examples applying these concepts to polling data about candidate preferences
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The document discusses the mean, variance, and standard deviation of binomial distributions. It provides examples of calculating these values for randomly guessing answers on a multiple choice test and polling voters with a presumed even split between two candidates. It concludes with homework problems involving binomial distributions.
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The document provides examples and step-by-step solutions to mathematical word problems involving functions, equations, and algebraic modeling. It includes 8 sample word problems, showing the work to determine an appropriate equation or function to model each problem and solve to find the unknown values. The overall goal is to help students analyze problems, determine solution strategies using algebra, and evaluate whether solutions make sense in context.
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This document provides instruction on combinations and permutations. It begins with examples of evaluating combinations and permutations, such as finding the number of combinations when choosing 3 items from a group of 8 items (8C3) or the number of permutations when selecting a preferred and substitute color from 12 color options (12P2). It then provides practice problems for students to determine whether a scenario involves combinations or permutations and write the appropriate expression to calculate the number of possibilities. The document aims to teach students the differences between combinations and permutations and how to set up and evaluate expressions to solve combinatorial problems.
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US Bancorp/DE operates as a bank holding company regulated under the Bank Holding Company Act and supervised by the Board of Governors of the Federal Reserve System. It owns several banking and non-banking subsidiaries across multiple states. The company was formed through a series of acquisitions and mergers of banks and mortgage companies dating back to 1983. It intends to split its banking subsidiaries into two separate publicly traded companies through a tax-free spin-off planned for April 1, 2000.
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(7) Lesson 9.2
The theoretical probability of rolling a sum of 10 when rolling two number cubes is 5/36.
There are 6 possible ways to roll a sum of 10: (1,9), (2,8), (3,7), (4,6), (5,5), (6,4).
There are 6 combinations that result in a sum of 10 out of the total possible combinations when rolling two number cubes, which is 6^2 = 36 possible outcomes.
Therefore, the theoretical probability is 5/36.
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The theoretical probability of rolling a sum of 10 when rolling two number cubes is 5/36.
There are 6 possible ways to roll a sum of 10: (1,9), (2,8), (3,7), (4,6), (5,5), (6,4).
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This document discusses statistics and probability concepts such as the fundamental counting principle, permutations, combinations, theoretical probability, and experimental probability. It provides examples of how to use these concepts to calculate the number of possible outcomes in probability experiments and real-world scenarios. For instance, it shows how to use permutations and combinations to determine the number of ways a student government can select officers from a group of people or how many combinations there are to draw a set of cubes from a bag. It also demonstrates calculating theoretical probabilities, such as the likelihood of rolling certain numbers on dice, and experimental probabilities based on data from trials.
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Top school in india
- 1. Top school in India By: school.edhole.com
- 2. Mean, Variance, and Standard Deviation for the binomial distribution For a binomial distribution, n p = × n p q = × × n p q 2 = × × m s s school.edhole.com
- 3. Example Randomly guessing on a 100 question multiple-choice test, where each question has 4 possible answers, = × = 4 25 = × × = 4 4.3 3 4 100 1 100 1 4 18.8 3 4 100 1 m 2 = × × = s s school.edhole.com
- 4. Example Using our range rule of thumb, m - s = - × = m s 2 25 2 4.3 16.4 + = + × = 2 25 2 4.3 33.6 It would be unusual to get less than 17 questions correct, or more than 33 question correct if you were randomly guessing on the test. school.edhole.com
- 5. Another Example You presume that people are evenly split (50/50) on their preference between two candidates. You poll 80 people, and find 45 prefer candidate A. Is this unexpected? We could find P(45 or more). Alternatively, using our presumed 50/50 preference, find mean=40, stddev=4.5. This suggests that outcomes of 31 to 49 would be usual occurrences. Since 45 falls in that range, we shouldn’t consider it unusual. school.edhole.com
- 6. Another Example Now suppose you poll 800 people, and 450 prefer candidate A. Is this unexpected? Using our presumed 50/50 preference, mean = 400, stddev = 14.1. Again using the range rule of thumb, this suggests that outcomes of 372 to 428 would be usual. Since the outcome of 450 is unusual, we should question whether our presumption of schoao l5.e0d/5h0o lsep.cliotm is accurate.
- 7. Homework 4.4: 1, 5, 7, 11, 13 school.edhole.com