Let Y be a random variable. In a population, μy 143 and oy = 51. Use the central limit theorem to answer the following questions. (Note: any intermediate results should be rounded to four decimal places) In a random sample of size n = 101, find Pr(Y <145). Pr(Y <145) = (Round your response to four decimal places)
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- Let X ∼ N (μ, 0.12). Now from sample of size n = 16, the sample mean is 5.038. Test, at significance level 5% and 10%, whether the population mean is 5 or larger.Let Y₁, Y₂, .. Yn denote a random sample from an exponential distribution with mean 0. a. Show that Ô1 = nY(1) and ĝ2 = Ỹ are unbiased estimators for 0. b. Find the efficiency of ₁ relative to 02. c. Which of these two estimators is superior?Use the central limit theorem to find the mean and standard error of the mean of the indicated sampling distribution. Then sketch a graph of the sampling distribution. The per capita consumption of red meat by people in a country in a recent year was normally distributed, with a mean of 114 pounds and a standard deviation of 39.2 pounds. Random samples of size 19 are drawn from this population and the mean of each sample is determined. μx=enter your response here σx=enter your response here (Round to three decimal places as needed.) Sketch a graph of the sampling distribution. Choose the correct graph below. A. 9.0 -105.0123.0 x A normal curve is over a horizontal x overbar axis labeled from negative 105.0 to 123.0 and is centered on 9.0. B. 114 87.0141.0 x A normal curve is over a horizontal x overbar axis labeled from 87.0 to 141.0 and is centered on 114. C.…
- Use the central limit theorem to find the mean and standard error of the mean of the indicated sampling distribution. Then sketch a graph of the sampling distribution. The per capita consumption of red meat by people in a country in a recent year was normally distributed, with a mean of 100 pounds and a standard deviation of 38.5 pounds. Random samples of size 18 are drawn from this population and the mean of each sample is determined. μx=nothingLet m denote margin of error, n sample size and σ standard deviation. m= zα/2(σn) Solve the above equation for n.Determine the minimum sample size required when you want to be 99% confident that the sample mean is within one unit of the population mean and σ=12.3. Assume the population is normally distributed.
- Suppose in a local Kindergarten through 12th grade (K -12) school district, 49% of the population favor a charter school for grades K through 5. A simple random sample of 144 is surveyed. a. Find the mean and the standard deviation of X of B(144, 0.49). Round off to 4 decimal places. O = b. Now approximate X of B(144, 0.49) using the normal approximation with the random variable Y and the table. Round off to 4 decimal places. Y - N( c. Find the probability that at most 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X 75) - P(Y > a (Z > e. Find the probability that exactly 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X = 81) - P(Use the data in the Excel workbook, on the worksheet labeled "Sample," for this question. The first column is just an observation index labeled i to name each observation. The observations are a simple random sample with replacement from a much larger population. The second column contains specific values y of a random variable Y found in some sampled population. The population standard deviation is not known to you, but it is known that Y has a Normal distribution in the sampled population. Compute the lower bound of an 85% confidence interval for the population mean of the random variable Y. i y 1 37 2 40 3 31 4 27 5 23 6 33 7 29 8 26 9 39 10 28 11 34 12 39 13 31 14 34 15 39 16 33 17 31 18 42Question 1 The Moment Generating Function (MGF) for a random variable X, mgfx(t) is given. Find the probability: P(|X|< 2) Hint: use the uniqueness theorem for MGFS. Simply speaking, if any two MGFS are same, then their distributions are also exactly same [Wikipedia] 1 e-20t 10 3 2 e4t + 10 mgfx (t) = -3t + + 5 est 5a sample is selected from a normal population with u=40 and σ =12. If the sample mean of M=36 corresponds to z=-2.00, then the sample size is n=64. is it true or falseSuppose in a local Kindergarten through 12th grade (K -12) school district, 49% of the population favor a charter school for grades K through 5. A simple random sample of 144 is surveyed. a. Find the mean and the standard deviation of X of B(144, 0.49). Round off to 4 decimal places. O = b. Now approximate X of B(144, 0.49) using the normal approximation with the random variable Y and the table. Round off to 4 decimal places. Y - N( c. Find the probability that at most 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X 75) - P(Y > a (Z > e. Find the probability that exactly 81 favor a charter school using the normal approximation and the table. (Round off to z-values up to 2 decimal places.) P(X = 81) - P(A random sample of size n1 =15 is selected from a normal population with a mean of 76 and standard deviation of 9. A second random sample size n2 =10 is taken from another normal population with mean 71 and a standard deviation 13. Let x barı and x bar2 be the sample means. Find: a. The probability that xbar1 – xbar2 exceeds 4.5 b. The probability that 3.5 s xbar1– xbar2 s 5.5SEE MORE QUESTIONSRecommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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