Let X, X3, and X, 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 u,, Hg, and u, and variances o,?, o,?, and o,, respectively. (Round your answers four decimal places.) n USE SALT (a) If #, = H2 = H3 = 70 and o,? = 0,² = 0,² = 18, calculate P(T, s 228) and P(174 s T, 5 228). P(T, S 228) = P(174 ST,S 228) = (b) Using the u's and o's given in part (a), calculate both P(64 s X) and P(68 s X S 72). P(64 sX) = P(68 sXS 72) = (c) Using the u's and a's given in part (a), calculate P(-12 s x, - 0.5x, - 0.5x, s 6). P(-12 sx, - 0.5x, - 0.5X, s 6) = | Interpret the quantity P(-12 s x, - 0.5x, - 0.5x, s 6). O The quantity represents the probability that the difference between X, and the sum of X, and X, is between -12 and 6. O The quantity represents the probability that the difference between x, and the sum of X, and X, is between -12 and habilit
Let X, X3, and X, 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 u,, Hg, and u, and variances o,?, o,?, and o,, respectively. (Round your answers four decimal places.) n USE SALT (a) If #, = H2 = H3 = 70 and o,? = 0,² = 0,² = 18, calculate P(T, s 228) and P(174 s T, 5 228). P(T, S 228) = P(174 ST,S 228) = (b) Using the u's and o's given in part (a), calculate both P(64 s X) and P(68 s X S 72). P(64 sX) = P(68 sXS 72) = (c) Using the u's and a's given in part (a), calculate P(-12 s x, - 0.5x, - 0.5x, s 6). P(-12 sx, - 0.5x, - 0.5X, s 6) = | Interpret the quantity P(-12 s x, - 0.5x, - 0.5x, s 6). O The quantity represents the probability that the difference between X, and the sum of X, and X, is between -12 and 6. O The quantity represents the probability that the difference between x, and the sum of X, and X, is between -12 and habilit
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Please solve (a) & (b) only! Thanks.
Transcribed Image Text:Let X,, X,, and X, 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 u,, l, and u, and variances o,2, o,2, and o,2, respectively. (Round your answers to
four decimal places.)
n USE SALT
(a) If u, = H, = l3 = 70 ando,
2
= 02
= 18, calculate P(T, S 228) and P(174 S T, S 228).
P(T, S 228) =
P(174 ST, S 228) =
(b) Using the u's and o's given in part (a), calculate both P(64 < X) and P(68 sXS 72).
P(64 s X) =
P(68 sXS 72) =
(c) Using the u's and o,'s given in part (a), calculate P(-12 < x, - 0.5X2 - 0.5X, s 6).
P(-12 s X, - 0.5X, – 0.5X3 < 6) =[
Interpret the quantity P(-12 s x, - 0.5X, - 0.5X3 s 6).
O The quantity represents the probability that the difference between X, and the sum of X, and x, is between -12 and 6.
O The quantity represents the probability that the difference between X, and the sum of X, and X, is between -12 and
6.
O The quantity represents the probability that the difference between X, and the average of X, and X, is between -12
and 6.
O The quantity represents the probability that X,, X,, and X, are all between -12 and 6.
O The quantity represents the probability that the difference between X, and the average of X, and X, is between -12
and 6.
(d) If u, = 30, µz = 40, µz = 50, o,² = 14, o,2 = 12, and o, = 10, calculate P(X, + X2 + X3 s 132) and also P(X, + X2 2 2X3).
P(X1 + X2 + X3 s 132) =
P(X, + X2 2 2X3) =
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