1. [10] Suppose that X ~N(-2, 4). Let Y = 3X-1. (a) Find the distribution of Y. Show your work. (b) Find P(-8< Y < 15) by using the CDF, (2), of the standard normal distribu- tion. (c) Find the 0.05th right-tail percentage point (i.e., the 0.95th quantile) of the distri- bution of Y.
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![1. [10] Suppose that X ~N(-2, 4). Let Y = 3X-1.
(a) Find the distribution of Y. Show your work.
(b) Find P(-8< Y < 15) by using the CDF, (2), of the standard normal distribu-
tion.
(c) Find the 0.05th right-tail percentage point (i.e., the 0.95th quantile) of the distri-
bution of Y.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff608d3a0-7ad6-4d87-98f1-9a851954d279%2F424ce2f8-a88d-40f2-9f12-b1c9e7c3fc40%2Fbusyepr_processed.jpeg&w=3840&q=75)
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- Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 46 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that ? = 7.80 ml/kg for the distribution of blood plasma. (d) Find the sample size necessary for a 99% confidence level with maximal margin of error E = 2.90 for the mean plasma volume in male firefighters. (Round up to the nearest whole number.) ________ male firefighters(d) For k satisfying -8 < k < k + 4 < 8, compute P(k < X < k + 4). (Round your answer to two decimal places.)A normal distribution has μ = 32 and σ = 5. (a) Find the z score corresponding to x = 27. (Enter an exact number.) -1 (b) Find the z score corresponding to x = 45. (Enter a number.) 2.6 (c) Find the raw score corresponding to z = -2. (Enter an exact number.) (d) Find the raw score corresponding to z = 1.1. (Enter a number.) Need Help? Submit Answer Read It
- Q1: Calculate the mean and the variance for Weibull Distribution when (i) a = 4,ẞ= 1 (ii) α = 1,ẞ = 4 Q2: Calculate the mean and the variance for Exponential Distribution when (i) a = 4,ẞ = 1 (ii) a = 1,ẞ= 4 Q3: Calculate the mean and the variance for Beta Distribution when (i) a = 4,ẞ= 1 (ii) a = 1,ẞ = 4Let X be a random variable that represents red blood cell count (RBC) in millions of cells per cubic millimeter of whole blood. Then X has a distribution that is approximately normal. For the population of healthy female adults, suppose the mean of the X distribution is about 4.84. Suppose that a female patient has taken six laboratory blood tests over the past several months and that the RBC count data sent to the patient's doctor are as follows. 4.2 4.4 4.3 4.1 4.8 4.9 (i) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.) x = s = (ii) Do the given data indicate that the population mean RBC count for this patient is lower than 4.84? Use ? = 0.05. (a) State the null hypotheses H0 and the alternate hypothesis H1 . H0 : ? H1 : ? (b) What is the value of the sample test statistic? (Round your answer to three decimal places.)(c) Compute the P-value. (Round your answer to four…Suppose X~N(19, 2.5). Find the 50th percentile.
- answer #5 onlyLet X be a random variable that represents red blood cell count (RBC) in millions of cells per cubic millimeter of whole blood. Then X has a distribution that is approximately normal. For the population of healthy female adults, suppose the mean of the X distribution is about 4.84. Suppose that a female patient has taken six laboratory blood tests over the past several months and that the RBC count data sent to the patient's doctor are as follows. 4.6 4.7 4.7 4.5 4.5 4.1 (i) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.) x = s = (ii) Do the given data indicate that the population mean RBC count for this patient is lower than 4.84? Use ? = 0.05. (a) State the null hypotheses H0 and the alternate hypothesis H1 . H0 : μ ---Select--- ≥ ≤ > ≠ < = H1 : μ ---Select--- ≠ < = ≥ > ≤ (b) What is the value of the sample test statistic? (Round your answer to three decimal places.)(c)…42. Consider the random variable (X, Y) of Exercise 9. (a) Find the curve of regression of X on Y. Is the regression linear? (b) Find the mean value of X when y = .5. (c) Find the curve of regression of Y on X. Is the regression linear? (d) Find the mean value of Y when x = .75.
- 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).(x₁,...,xn) be a data set, and denote its sample standard deviation with s. Let yį = ax; + b. (a) Show that sy = |a|sx, where sy is the sample standard deviation of y = (y₁,..., Yn). (b) Show that Median(y) = a. Median(x) + b. Let x = (c) If a > 0, can you write the relation between Q1(y) and Q1(x)? What happens if a < 0? Note: Q1(x) (or Q1(y)) denotes the first quartile of the distribution of the random variable x (or y)Suppose a sample Y1, ..., Yn is selected from an exponential distribution with E (Yi) = θ and V (Yi) = θ2. Let θˆ be an estimator of the mean, θ.1. Explain what a parameter is. What is the parameter of interest in this case?2. Name the properties of a good estimator and explain, shortly, what is meant by each. (a)(b) (c)3. Given the properties you discussed in (2) and the parameter of interest identified in (1), what estimator would you propose?4. What would the sampling distribution of this estimator be? Why?
