- Due 05 04 2022 Use The Following Information For The Following Problems 20 05 1 64 20 025 1 96 20 01 2 32 To 0 1 (60.58 KiB) Viewed 24 times
Due 05/04/2022 Use the following information for the following problems. 20.05 = 1.64, 20.025 = 1.96, 20.01 = 2.32. to.05,9 = 1.83, 10.025.9 = 2.26, 10.019 = 2.82. t0.05.10 = 1.81, to.025,10 2.22, +0.01.10 = 2.76. 70.05.11 = 1.79, 70,025,11 = 2.20, t0.01.11 = 2.72. Problem 1 The inside diameter of a randomly selected piston ring is a normal random variable with mean value 12 cm and standard deviation 0.04 cm. • Calculate P(11.99 < X < 12.01) when n 16. Refer to the z-table. • How likely is it that the sample mean diameter exceeds 12.01 when n = 25? Refer to the z-table. Problem 2 A shipping company handles containers in three different sizes. Let X, (i=1,2,3) denote the number of type i containers shipped during a given week. Suppose E(X) = 200, E(X2) = 250, E(X3) = 100, Var(X1) = 10, Var(X2) = 12, Var(X3) = 8. • Assume that X1, X2, X3 are independent. Calculate the expected value and variance of Y = 27X1 + 125X2 + 512X3. . Would your calculations necessarily be correct if the X's were not inde pendent? Explain.