
(a) If μ1=μ2=μ3=80 and σ12=σ22=σ32=15, calculate P(To≤260) and P(210≤To≤260). P(To≤260)=P(210≤To≤260)= (b) Using the μi′ 's and σi′ 's given in part (a), calculate both P(75≤Xˉ) and P(78≤Xˉ≤82). P(75≤Xˉ)= P(78≤Xˉ≤82)= (c) Using the μi′ 's and σi′ 's given in part (a), calculate P(−10≤X1−0.5X2−0.5X3≤5). P(−10≤x1−0.5x2−0.5x3≤5)= Interpret the quantity P(−10≤x1−0.5x2−0.5x3≤5). The quantity represents the probability that the difference between x1 and the average of x2 and x3 is between -10 and 5 . The quantity represents the probability that the difference between x3 and the sum of x1 and x2 is between -10 and 5 . The quantity represents the probability that the difference between x1 and the sum of x2 and x3 is between -10 and 5 . The quantity represents the probability that the difference between x3 and the average of x1 and x2 is between -10 and 5 . The quantity represents the probability that x1,x2, and x3 are all between -10 and 5 . (d) If μ1=30,μ2=40,μ3=50,σ12=12,σ22=14, and σ32=10, calculate P(x1+x2+x3≤130) and also P(x1+x2≥2x3)P(x1+X2+x3≤130)=P(x1+x2≥2x3)= You may need to use the appropriate table in the Appendix of Tables to answer this question.