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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)
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.

Let \( X_1, X_2, \) and \( X_3 \) represent the times necessary to perform three successive repair tasks at a certain service facility. Suppose they are independent, normal r.v’s with expected values \( \mu_1, \mu_2, \) and \( \mu_3 \) and variances \( \sigma_1^2, \sigma_2^2, \) and \( \sigma_3^2 \) respectively. (Round your answers to four decimal places.) --- ### (a) If \( \mu_1 = \mu_2 = \mu_3 = 70 \) and \( \sigma_1^2 = \sigma_2^2 = \sigma_3^2 = 18 \), calculate \( P(T_0 \le 228) \) and \( P(174 \le T_0 \le 228) \). - \( P(T_0 \le 228) = \) \(\underline{\hspace{2cm}}\) - \( P(174 \le T_0 \le 228) = \) \(\underline{\hspace{2cm}}\) --- ### (b) Using the \( \mu_i \)’s and \( \sigma_i^2 \)’s given in part (a), calculate both \( P(64 \le \overline{X} \)) and \( P(68 \le \overline{X} \le 72) \). - \( P(64 \le \overline{X}) = \) \(\underline{\hspace{2cm}}\) - \( P(68 \le \overline{X} \le 72) = \) \(\underline{\hspace{2cm}}\) --- ### (c) Using the \( \mu_i \)’s and \( \sigma_i^2 \)’s given in part (a), calculate \( P(-12 \le X_1 - 0.5X_2 - 0.5X_3 \le 6) \). - \( P(-12 \le X_1 - 0.5X_2 - 0.5X_3 \le 6) = \) \(\underline{\hspace{2cm}}\) #### Interpret the quantity \( X_1 - 0.5X_2 - 0.5
Transcribed Image Text:Let \( X_1, X_2, \) and \( X_3 \) represent the times necessary to perform three successive repair tasks at a certain service facility. Suppose they are independent, normal r.v’s with expected values \( \mu_1, \mu_2, \) and \( \mu_3 \) and variances \( \sigma_1^2, \sigma_2^2, \) and \( \sigma_3^2 \) respectively. (Round your answers to four decimal places.) --- ### (a) If \( \mu_1 = \mu_2 = \mu_3 = 70 \) and \( \sigma_1^2 = \sigma_2^2 = \sigma_3^2 = 18 \), calculate \( P(T_0 \le 228) \) and \( P(174 \le T_0 \le 228) \). - \( P(T_0 \le 228) = \) \(\underline{\hspace{2cm}}\) - \( P(174 \le T_0 \le 228) = \) \(\underline{\hspace{2cm}}\) --- ### (b) Using the \( \mu_i \)’s and \( \sigma_i^2 \)’s given in part (a), calculate both \( P(64 \le \overline{X} \)) and \( P(68 \le \overline{X} \le 72) \). - \( P(64 \le \overline{X}) = \) \(\underline{\hspace{2cm}}\) - \( P(68 \le \overline{X} \le 72) = \) \(\underline{\hspace{2cm}}\) --- ### (c) Using the \( \mu_i \)’s and \( \sigma_i^2 \)’s given in part (a), calculate \( P(-12 \le X_1 - 0.5X_2 - 0.5X_3 \le 6) \). - \( P(-12 \le X_1 - 0.5X_2 - 0.5X_3 \le 6) = \) \(\underline{\hspace{2cm}}\) #### Interpret the quantity \( X_1 - 0.5X_2 - 0.5
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