28. Let X1, X2, and X3 represent the times necessary to perform three successive repair tasks at a certain service facility. Suppose they are independent, normal rv s with expected values m1, m2, and m3 and variances ,and , respectively.

a. If m  m2  m3  60 and , calculate P(X1  X2  X3 200). What is P(150 X1  X2  X3 200)?

b. Using the mi s and si s given in part (a), calculate and .

c. Using the mi s and si s given in part (a), calculate P(10 X1  .5X2  .5X3 5).

d. If m140, m250, m360, , , and , calculate P(X1  X2  X3 160)

and P(X1  X2  2X3).

s23

 14 s22 s  12 21

 10 P155 X2 P158 X

622 s21

 s22

 s23

 15 s23s21

, s22 s2i

 V1Xi 2