Let Xg, 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 44. Hz, and iz and variances o,?, o,?, and o,?, respectively. (Round your answers to four decimal places.) A USE SALT (a) If Hy = H2 = H3 = 60 and o,? - 0,? - 0,² - 18, calculate P(T, s 204) and P(144 s T, s 204). P(T, s 204) = 0.005 P(144 s T, s 204) = (b) Using the 4's and a's given in part (a), calculate both P(54 sÃ) and P(58 sis 62). P(54 s ) = 0.508 P(58 s Xs 62) 0.588 (c) Using the u's and o's given in part (a), calculate P(-12 s X, - 0.5X2 - 0.5X3 s 6). P(-12 s X, - 0.5x2 - 0.5X, s 6) = 0.8005
Let Xg, 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 44. Hz, and iz and variances o,?, o,?, and o,?, respectively. (Round your answers to four decimal places.) A USE SALT (a) If Hy = H2 = H3 = 60 and o,? - 0,? - 0,² - 18, calculate P(T, s 204) and P(144 s T, s 204). P(T, s 204) = 0.005 P(144 s T, s 204) = (b) Using the 4's and a's given in part (a), calculate both P(54 sÃ) and P(58 sis 62). P(54 s ) = 0.508 P(58 s Xs 62) 0.588 (c) Using the u's and o's given in part (a), calculate P(-12 s X, - 0.5X2 - 0.5X3 s 6). P(-12 s X, - 0.5x2 - 0.5X, s 6) = 0.8005
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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Transcribed Image Text:(d) If u, = 30, µ, = 40, µz = 50, o,
14, 02
2
= 10, and o,
= 12, calculate P(X, + X, + X3 s 132) and also P(X, + X2 2 2X3).
=
P(X, + X2 + X3 s 132)
P(X, + X2 2 2X3)
0.0001
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 4,, Hz, and uz and variances o,2, 0,2, and o,2, respectively. (Round your answers to four decimal places.)
A USE SALT
2
(a) If H1 = H2 = H3 = 60 and o,? = 0,2 .
= 18, calculate P(T, s 204) and P(144 s T, s 204).
P(T, s 204) =
0.9995
P(144 s T,s 204) =
(b) Using the us and os given in part (a), calculate both P(54 s X) and P(58 s Xs 62).
P(54 s X)
P(58 s Xs 62) = 0.568
0.568
%3D
(c) Using the u's and o's given in part (a), calculate P(-12 s X, - 0.5X2 - 0.5X3 s 6).
P(-12 s X, - 0.5X, - 0.5x, s 6) = 0.8665
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