Let X1, X2, and X3 represent the times necessary to perform three successive repair tasks at a service facility. Suppose they are independent, normal rv's with expected values µ1, H2, and µz and var- iances o?, o3, and o, respectively.

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28. Let X1, X2, and X3 represent the times necessary to
perform three successive repair tasks at a service
facility. Suppose they are independent, normal
rv's with expected values l1, µ2, and µ3 and var-
iances of, ož, and oz, respectively.
а. If
and of = o3 =
Hi = µ2 = µ3 = 60
o = 15, calculate P(X1 + X2 + X3 < 200).
What is P(150 < X1 + X2 + X3 < 200)?
b. Using the u;'s and o;'s given in part (a), calcu-
late P(55 < X) and P(58 < X < 62).
c. Using the u;'s and o;'s given in part (a), calcu-
late P(-10 < X -.5X2 — .5Xз < 5).
d. If M 3 40, 12 — 50, Из — 60, от — 10,
o3 = 12, and o = 14
X2 + X3 < 160) and P(X1 + X2 > 2X3).
여= 10,
calculate P(X1 +
Transcribed Image Text:28. Let X1, X2, and X3 represent the times necessary to perform three successive repair tasks at a service facility. Suppose they are independent, normal rv's with expected values l1, µ2, and µ3 and var- iances of, ož, and oz, respectively. а. If and of = o3 = Hi = µ2 = µ3 = 60 o = 15, calculate P(X1 + X2 + X3 < 200). What is P(150 < X1 + X2 + X3 < 200)? b. Using the u;'s and o;'s given in part (a), calcu- late P(55 < X) and P(58 < X < 62). c. Using the u;'s and o;'s given in part (a), calcu- late P(-10 < X -.5X2 — .5Xз < 5). d. If M 3 40, 12 — 50, Из — 60, от — 10, o3 = 12, and o = 14 X2 + X3 < 160) and P(X1 + X2 > 2X3). 여= 10, calculate P(X1 +
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