Let X be distributed according to a normal law with mean µ = 0 and unknown variance o². Find o? given that Prob(|X|<0.5) = 0.3 %3D
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- A food manufacturer claims that eating its new cereal as part of a daily diet lowers total blood cholesterol levels. The table shows the total blood cholesterol levels (in milligrams per deciliter of blood) of seven patients before eating the cereal and after one year of eating the cereal as part of their diets. Use technology to test the mean difference. Assume the samples are random and dependent, and the population is normally distributed. At α = 0.05, can you conclude that the new cereal lowers total blood cholesterol levels? Patient 1 2 3 4 5 6 7 Total Blood Cholesterol (Before) 205 220 240 235 250 270 230 Total Blood Cholesterol (After) 196 217 242 232 245 267 225 Let the blood cholesterol level before eating the cereal be population 1. Let the blood cholesterol level after eating the cereal be population 2. Identify the null and alternative hypotheses, where μμ₁ −μ₂. Choose the correct answer below. A. Ho: Hd #0 HA: Hd=0 B. Ho: Hd ≤0 HA: Md>0 C. Ho: Hd = 0 HA: Md #0 D. Ho: Hd 20…For mated pairs of gallinules (type of water bird), let X equal the weight in grams of the male and Y the weight in grams of the female. Assume that X and Y have a bivariate normal distribution with #x = 415, o = 611, y = 347 and o=689. The correlation coefficient between X and Y is p = -0.25. (b) Determine the marginal distributions of X and then of Y. (c) Find the conditional distribution of Y|X = x. (d) Find E(Y|X = z) and Var(Y|X = x).Suppose you fit a simple Poisson model such that in A = XB where B = 1.9. What would the variance be if x = -0.8 ?
- Suppose, household color TVs are replaced at an average age of μ = 9.0 years after purchase, and the (95% of data) range was from 5.8 to 12.2 years. Thus, the range was 12.2 − 5.8 = 6.4 years. Let x be the age (in years) at which a color TV is replaced. Assume that x has a distribution that is approximately normal. (a) The empirical rule indicates that for a symmetric and bell-shaped distribution, approximately 95% of the data lies within two standard deviations of the mean. Therefore, a 95% range of data values extending from μ − 2σ to μ + 2σ is often used for "commonly occurring" data values. Note that the interval from μ − 2σ to μ + 2σ is 4σ in length. This leads to a "rule of thumb" for estimating the standard deviation from a 95% range of data values. Estimating the standard deviationFor a symmetric, bell-shaped distribution, standard deviation ≈ range 4 ≈ high value − low value 4 where it is estimated that about 95% of the commonly occurring data…The dependent is variance inflation factor, make a decision whether it need to drop any variables.Daily sales of a store is normally distributed with mean μ=180 Rials and variance σ2 =100. Find the probability that total sales over a period of nine days is more than 1800 Rials.
- It has been determined experimentally that steel wires of a certain length have strength with a mean value of 1 kip and a coefficient of variation of 16%. What is the probability that the strength of such a wire is less than 0.7 kips? Try Type I and Type III asymptotic distributions of extremes and compare the results.A food manufacturer claims that eating its new cereal as part of a daily diet lowers total blood cholesterol levels. The table shows the total blood cholesterol levels (in milligrams per deciliter of blood) of seven patients before eating the cereal and after one year of eating the cereal as part of their diets. Use technology to test the mean difference. Assume the samples are random and dependent, and the population is normally distributed. At α=0.05, can you conclude that the new cereal lowers total blood cholesterol levels? Patient 1 2 3 4 5 6 7 Total Blood Cholesterol (Before) 215 225 235 240 255 260 225 Total Blood Cholesterol (After) 214 222 240 237 254 257 222 Let the blood cholesterol level before eating the cereal be population 1. Let the blood cholesterol level after eating the cereal be population 2. Identify the null and alternative hypotheses, where μd=μ1−μ2. Choose the correct…I For Poisson's distribution prove that Variance =