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- 16. Let X be normally distributed with mean μ = 120 and standard deviation σ = 20. a. Find P(X86). b. Find P(80 ≤x≤ 100). ة ن فـ d. Find x such that P(X ≤x) = 0.40. Find x such that P(X>x) = 0.90.6 The blood pressure of a diabetic taken at random has a normal distribution with mean 126 and variance 60. The blood pressure of a non-diabetic taken at random has a normal distribution with mean 121 and variance 40. Let X d be the average blood pressure of four diabetics taken at random and X n be the average blood pressure of four non-diabetics taken at random. Find Prob( X d > X n). Hint: Define D by D= X d - X n, find the mean and the variance of D and then calculate the probability that D>0.3. Let X Pois(4). Find the distribution of Y = √X.
- 2. Suppose that X1, X2, X3 and X4, are independent and identically distributed with a mean of 2.5 and a standard deviation of 0.6. Find the mean and standard deviation for variables Y and W defined below. Let Y= 4X1 а. b. Let W= Xi + X2 + X3 + X427. Let X denote the proportion of allotted time that a randomly selected student spends working on a certain aptitude test. Suppose the pdf of X is f(x; 0) = (0+1)xº 0≤x≤1 for some > -1. A random sample of ten students yields data x₁ = .92, x₂ = .79, X3 = .90, X4 = .65, x5 = .86, x6 = .47, X7 = .73, x8 = .97, x9 = .94, X10 = .77. a. Use the method of moments to obtain an estimator of 0, and then compute the estimate for this data. b. Obtain the maximum likelihood esti- mator of 0, and then compute the esti- mate for the given data.3. A bank teller serves customers standing in the queue one by one. Suppose that the service time X; for customer i has mean E(X;) = 2 minutes and variance V(X;) = 1. We assume that service times for different bank customers are independent. Let Y be the total time the bank teller spends serving 50 customers. Find P(90 < Y < 110). 4. Derive the mean and variance of the t distribution. 5. Suppose that X1, X2, · , Xm and Y1, Y2, , Yn are independent random samples from N (µx, o) and N(uy, o3), respectively. a. Find E(X –Ỹ). b. Find V(X – Y)
- For any variable X, if: the standard deviation = and the variance = Var(X) Which of the following statement is true: Select one: a. SD < Var(X) O b. (SD)² = Var(X) (SD) C. SD = [var(x)]²26. Let x represent the number of underinflated tires on an automobile. a. Which of the following p(x) functions specifies a legitimate distribution for x, and why are the other two not legitimate? (i) p(0) 5.3, p(1) 5 .2, p(2) 5 .1, p(3) 5 .05, p(4) 5 .05 (ii) p(0) 5 .4, p(1) 5 p(2) 5 p(3) 5 .1, p(4) 5 .3 (iii) p(x) 5 .2(3 2 x) for x 5 0, 1, 2, 3, 4 b. For the legitimate distribution of part (a), determine the long-run proportion of cars having at most two underinflated tires, the proportion having fewer than two underinflated tires, and the proportion having at least one underinflated tire.Suppose there is a test, φ, that yields the distribution of test outcomes for good drugs and bad drugs seen in the Figure. In this case, is it possible to create a rule for accepting and rejecting drugs that yields no Type I or Type II error? If so, be sure to show this threshold rule explicitly on the graph above. If not, explain why this is impossible.
- I need help with parts “c”, “d, and “e” thanks.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 38.6 pounds. Random samples of size 20 are drawn from this population and the mean of each sample is determined. ux= o-x= graph=2. Let X - tp. Verify the mean and variance formulas. (Hint: Let X = p/2UV-1/2.)