Let x,, 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 u, H2, and u3 and variances a,?, a,?, and a,, respectively. (Round your answers to four decimal places.) In USE SALT (a) If 4, = H2 = H3 = 90 and a,2 = a,2 = 0,? = 15, calculate P(T, < 290) and P(240 ST, S 290). P(T, s 290) = P(240 s T, s 290) = (b) Using the u,'s and o's given in part (a), calculate both P(85 s X) and P(88 s Xs 92). P(85 s X) P(88 sXS 92) (c) Using the u,'s and a's given in part (a), calculate P(-10 s X, - 0.5X2 - 0.5X3 s 5). P(-10 s x, - 0.5X2 - 0.5X, s 5) = Interpret the quantity P(-10 s x, - 0.5X2 - 0.5X3 s 5). The quantity represents the probability that X,, X,, and X, are all between -10 and 5. The quantity represents the probability that the difference between X, and the sum of X, and X, is between -10 and 5. The quantity represents the probability that the difference between X, and the average of X2 and X, is between -10 and 5. The quantity represents the probability that the difference between X, and the sum of X, and X, is between - 10 and 5. The quantity represents the probability that the difference between X, and the average of X, and X, is between -10 and 5. (d) If = 50, 42 = 60, 4z = 70, o,2 = 10, o,? = 12, and a,? = 14, calculate P(x, + X, + X3 s 190) and also P(X1 + X2 2 2X3). P(X, + X2 + X3 s 190) P(X1 + X2 2 2X3) You may need to use the appropriate table in the Appendix of Tables to answer this question.
Let x,, 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 u, H2, and u3 and variances a,?, a,?, and a,, respectively. (Round your answers to four decimal places.) In USE SALT (a) If 4, = H2 = H3 = 90 and a,2 = a,2 = 0,? = 15, calculate P(T, < 290) and P(240 ST, S 290). P(T, s 290) = P(240 s T, s 290) = (b) Using the u,'s and o's given in part (a), calculate both P(85 s X) and P(88 s Xs 92). P(85 s X) P(88 sXS 92) (c) Using the u,'s and a's given in part (a), calculate P(-10 s X, - 0.5X2 - 0.5X3 s 5). P(-10 s x, - 0.5X2 - 0.5X, s 5) = Interpret the quantity P(-10 s x, - 0.5X2 - 0.5X3 s 5). The quantity represents the probability that X,, X,, and X, are all between -10 and 5. The quantity represents the probability that the difference between X, and the sum of X, and X, is between -10 and 5. The quantity represents the probability that the difference between X, and the average of X2 and X, is between -10 and 5. The quantity represents the probability that the difference between X, and the sum of X, and X, is between - 10 and 5. The quantity represents the probability that the difference between X, and the average of X, and X, is between -10 and 5. (d) If = 50, 42 = 60, 4z = 70, o,2 = 10, o,? = 12, and a,? = 14, calculate P(x, + X, + X3 s 190) and also P(X1 + X2 2 2X3). P(X, + X2 + X3 s 190) P(X1 + X2 2 2X3) You may need to use the appropriate table in the Appendix of Tables to answer this question.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.2: The Least Square Line
Problem 5E
Related questions
Question
Transcribed Image Text:Let x,, 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 u, H2, and u3 and variances a,?, a,?, and az?, respectively. (Round your
answers to four decimal places.)
In USE SALT
(a) If 4, = H2 = H3 = 90 and a,2 = a,? = a,? = 15, calculate P(T, < 290) and P(240 ST, s 290).
P(T, S 290) =
P(240 < T, s 290) =
(b) Using the u,'s and o's given in part (a), calculate both P(85 s X) and P(88 s Xs 92).
P(85 s X)
P(88 sXS 92)
(c) Using the u,'s and a's given in part (a), calculate P(-10 s X, - 0.5X2 - 0.5X3 s 5).
P(-10 s X, - 0.5X2 - 0.5X3 s 5) =
Interpret the quantity P(-10 s x, - 0.5X2 - 0.5X3 s 5).
The quantity represents the probability that X,, X2, and X, are all between -10 and 5.
The quantity represents the probability that the difference between X, and the sum of X, and X, is between -10 and
5.
The quantity represents the probability that the difference between X, and the average of X, and X3 is between -10
and 5.
The quantity represents the probability that the difference between X, and the sum of X, and X, is between -10 and
5.
The quantity represents the probability that the difference between X, and the average of X, and X, is between -10
and 5.
(d) If , = 50, 42 = 60, µ3 = 70, a,? = 10, o,? = 12, and a,? = 14, calculate P(X, + X, + X3 s 190) and also
P(X1 + X2 2 2X3).
P(X, + X2 + X3 s 190)
P(X1 + X2 2 2X3)
You may need to use the appropriate table in the Appendix of Tables to answer this question.
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