Let X1, X2, and X3 represent the times necessary to perform three successive repair tasks at a service facility. Suppose they are independent, normal rvs with expected values μ1, μ2, and μ3 and variances σ1 2, σ2 2, and σ3 2, respectively. (a) If μ1 ¼ μ2 ¼ μ3 ¼ 60 and σ1 2 ¼ σ2 2 ¼ σ3 2 ¼ 15, calculate P(X1 + X2 + X3 200). (b) Using the μis and σis given in part (a), what is P(150 X1 + X2 + X3 200)? (c) Using the μis and σis given in part (a), calculate P 55 XðÞand P 58 X 62 at the beginning of this section, Xdenotes the sample mean, so here X ¼ X1 þ X2 þ X3ðÞ=3:] ðÞ: [As noted (d) Using the μis and σis given in part (a), calculate P(–10 X1 .5X2 .5X3 5). (e) If μ1 ¼ 40, μ2 ¼ 50, μ3 ¼ 60, σ1 P(X1 + X2 + X3 160) and P(X1 +X2 2X3).