# Question: Let Y X1 X2

Let Y = X1 + X2 + · · · + X15 be the sum of a random sample of size 15 from the distribution whose pdf is f(x) = (3/2)X2, −1 < x < 1. Using the pdf of Y, we find that P(−0.3 ≤ Y ≤ 1.5) = 0.22788. Use the central limit theorem to approximate this probability

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Approximate P(39.75 ≤ X ≤ 41.25), where X is the mean of a random sample of size 32 from a distribution with mean μ = 40 and variance σ2 = 8. A die is rolled 24 independent times. Let Y be the sum of the 24 resulting values. 0Recalling that Y is a random variable of the discrete type, approximate (a) P(Y ≥ 86). (b) P(Y < 86). (c) P(70 < Y ≤ 86). If E(X) = 17 and E(X2) = 298, use Chebyshev’s inequality to determine (a) A lower bound for P(10 < X < 24). (b) An upper bound for P(|X − 17| ≥ 16). A small part for an automobile rearview mirror was produced on two different punch presses. In order to describe the distribution of the weights of those parts, a random sample was selected, and each piece was weighed in ...In the expression for gr(y) = G’r(y) in Equation 6.3-1, let n = 6, and r = 3, and write out the summations, showing that the “telescoping” suggested in the text is achieved. In equation 6.3-1Post your question