11/18/2023 0 Comments Lesson 8.6 anyway you slice it![]() ![]() If you cut a slice of pizza, each slide would probably be a sector of a circle. © Texas Education Agency (TEA).- E N D - Presentation Transcript Use the information below to generate a citation. Then you must include on every digital page view the following attribution: If you are redistributing all or part of this book in a digital format, Then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a print format, Changes were made to the original material, including updates to art, structure, and other content updates. Want to cite, share, or modify this book? This book uses theĪnd you must attribute Texas Education Agency (TEA). See The Normal Distribution for help with calculator instructions.įor Part (a), you include 150 so P( X ≥ 150) has a normal approximation P( Y ≥ 149.5) = 0.8641. The random variable for the normal distribution is Y. The mean is 159, and the standard deviation is 8.6447. The formulas for the mean and standard deviation are μ = np and σ = n p q n p q. Because np > 5 and nq > 5, use the normal approximation to the binomial. Let X = the number that favor a charter school for grades K through 5. Find the probability that exactly 175 favor a charter school.Find the probability that fewer than 147 favor a charter school.Find the probability that more than 155 favor a charter school.Find the probability that at most 160 favor a charter school.Find the probability that at least 150 favor a charter school.A simple random sample of 300 is surveyed. Suppose in a local kindergarten through 12 th grade (K–12) school district, 53 percent of the population favor a charter school for grades K through 5. The number 0.5 is called the continuity correction factor and is used in the following example. We subtract 0.5 if we are looking for the probability that is greater than or equal to that number. We add 0.5 if we are looking for the probability that is less than or equal to that number. So, for whatever value of x we are looking at (the number of successes). In order to get the best approximation, add 0.5 to x or subtract 0.5 from x (use x + 0.5 or x – 0.5). Then the binomial can be approximated by the normal distribution with mean μ = np and standard deviation σ = n p q n p q. ![]() The product >5 is more or less accepted as the norm here.). To ensure this, the quantities npĪnd nq must both be greater than five ( np > 5 and nq > 5 the approximation is better if they are both greater than or equal to 10. Similar to the shape of the normal distribution. The shape of the binomial distribution needs to be Recall that if X is the binomial random variable, then X ~ B( n, p). Each trial has the same probability of a success, p.The outcomes of any trial are success or failure.There are a certain number, n, of independent trials.You must meet the following conditions for a binomial distribution: To compute the normal approximation to the binomial distribution, take a simple random sample from a population. Using the normal approximation to the binomial distribution simplified the process. To calculate the probabilities with large values of n, you had to use the binomial formula, which could be very complicated. Binomial probabilities with a small value for n (say, 20) were displayed in a table in a book. Historically, being able to compute binomial probabilities was one of the most important applications of the central limit theorem. ![]()
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