A Show 1. Can you help me explain the usefulness of Central Limit Theorem in solving problems involving sampling. And also the importance of the use of CLT in our daily life by creating own word problem, or formulating a new word problem. 2. There are 250 dogs at a dog show that weigh an average of 12 pounds, with a standard deviation of 8 pounds. If 4 dogs are chosen at random, what is the probability that the average weight is greater than 8 pounds? 3. The number of driving miles before a certain kind of tire begins to show wear is on the average, 16,800 miles with a standard deviation of 3, 300 miles. a. What is the probability that the 36 tires will have an average of less than 16,000 miles until the tires begin to wear out? b. What is the probability that the 36 tires will have an average of more than 18,000 miles until the tires begin to wear out? 4. The average number of milligrams of cholesterol in a cup of certain brand of ice cream is 660 mg, the standard deviation is 35 mg. Assume the variable is normally distributed. a. If a cup of ice cream is selected, what is the probability that the cholesterol content will be more than 670mg? b. If a sample of 10 cups of ice cream is selected, what is the probability that mean of the sample will be larger than 670 mg? 5. In a study of the life expectancy of 400 people in a certain geographic region, the mean age at death was 70 years, and the standard deviation was 5.1 years. If a sample of 50 people from this region is selected, what is the probability that the mean life expectancy will be less than 68 years? 6. The average cholesterol content of a certain canned goods is 215 milligrams, and the standard deviation is 15 milligrams. Assume that the variable is normally distributed. If a sample of 25 canned goods is selected, what is the probability that the mean of the sample will be greater than 220 milligrams? 7. The average public elementary school has 486 students with a standard deviation of 87. If a random sample of 38 public elementary schools is selected, what is the probability that the number of students enrolled is between 445 and 485? Answer & Explanation  Rated Helpful <p>usce dui lectus, congue vel laoreet ac, dictum vitae odio. Donec aliquet. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Nam lacinia pulvinar tortor nec facilisis. Pellentesque dapibus efficitur laoreet. Nam risus ante, dapibus a molestie consequ</p> Fusce dui lectus, congue vel laoreet ac, dictum vitae odio. Donec aliquet Unlock full access to Course Hero Explore over 16 million step-by-step answers from our library Subscribe to view answer Pellentesque dapibus efficitur laoreet. Nam risus ante, dapibus a molestie consequat, ultrices ac magna. Fusce dui lectus, congue vel laoreet ac, dictum vitae odio. Donec aliquet. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Nam lacinia pulvinar tortor nec facilisis. Pellent at, ultrices ac magna. Fusce dui lec lestie consequat, ultrice gue ec facilisis. Pellentesque dapibus e gue ipiscing elit. Fusce dui lectus, o. Donec aliquet. L gue onec aliquet. risus ante, dapibu icitur laoreet. Nam gue icitur laoreet. Nam risus ante, gue et, consectetur adipiscing elit. gue icitur laoreet. Nam risus ante, d gue sum dolor sit amet, consectetur adipiscing elit. Nam lacinia pulvinar tortor nec facilisis. Pellentesque dapibus efficitur laor jpg jpg jpg jpg jpg jpg jpg Student reviews 100% (7 ratings) Thorough explanation Easy to follow Clear formatting Why is central limit theorem useful in solving problems that involves sampling?The central limit theorem is useful when analyzing large data sets because it allows one to assume that the sampling distribution of the mean will be normally-distributed in most cases. This allows for easier statistical analysis and inference.
What is the central limit theorem and how is it useful?What is the Central Limit Theorem? The CLT is a statistical theory that states that - if you take a sufficiently large sample size from a population with a finite level of variance, the mean of all samples from that population will be roughly equal to the population mean.
What is the importance of the use of central limit theorem in our daily life?Biologists use the central limit theorem whenever they use data from a sample of organisms to draw conclusions about the overall population of organisms. For example, a biologist may measure the height of 30 randomly selected plants and then use the sample mean height to estimate the population mean height.
What does the central limit theorem says about sampling distribution?The central limit theorem says that the sampling distribution of the mean will always be normally distributed, as long as the sample size is large enough. Regardless of whether the population has a normal, Poisson, binomial, or any other distribution, the sampling distribution of the mean will be normal.
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Explain the usefulness of the central Limit Theorem in solving problems involving sampling
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