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(To  200) and P(150  To  200)?

b. Using the mi

’s and si

’s given in part (a), calculate both P(55  ) and P(58   62).

c. Using the mi

’s and si

’s given in part (a), calculate and interpret P(10  X1  .5X2  .5X3  5).

d. If m1 40, m2 50, m3 60, , s and 1 2 5 10, s2 2 5 12 X X s1 2 5 s2 2 5 s3 2 5 15 s3 s 2 1 2

, s2 2

si 2 5 V(Xi

)

, calculate P(X1 X2 X3  160) and also P(X1 X2  2X3).