Let X, X2, 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. lg, and ug and variances o,, o,, and o, respectively. (Round your answers to four decimal places.) A USE SALT
Let X, X2, 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. lg, and ug and variances o,, o,, and o, respectively. (Round your answers to four decimal places.) A USE SALT
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Please solve (b), (c), and (d) 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 random variables 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.)
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### (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 \( P(174 \le T_0 \le 228) \).
- \( P(T_0 \le 228) = \) [Input box]
- \( P(174 \le T_0 \le 228) = \) [Input box]
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### (b)
Using the \(\mu_i\) s and \(\sigma_i\) s given in part (a), calculate both \( P(64 \le \bar{X} \) and \( P(68 \le \bar{X} \le 72) \).
- \( P(64 \le \bar{X}) = \) [Input box]
- \( P(68 \le \bar{X} \le 72) = \) [Input box]
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### (c)
Using the \(\mu_i\) s and \(\sigma_i\) s given in part (a), calculate \( P(-12 \le X_1 - 0.5X_2 - 0.5X_3 \le 6) \).
\[ P(-12 \le X_1 - 0.5X_2 - 0.5X_3 \le 6) = \] [Input box]
#### Interpret the quantity \( X_1 - 0.5X_2 - 0.5X_3 \).
- [ ] The quantity represents the probability that the difference between \( X_3 \) and the sum of \( X_1 \) and \( X_2 \) is between \(-12\)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc32f563a-6b55-4123-a4c3-1254c39a7403%2F682a9fd6-2d0d-487e-8aff-858753e0b131%2F3mwpfcn_processed.png&w=3840&q=75)
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 random variables 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 \( P(174 \le T_0 \le 228) \).
- \( P(T_0 \le 228) = \) [Input box]
- \( P(174 \le T_0 \le 228) = \) [Input box]
---
### (b)
Using the \(\mu_i\) s and \(\sigma_i\) s given in part (a), calculate both \( P(64 \le \bar{X} \) and \( P(68 \le \bar{X} \le 72) \).
- \( P(64 \le \bar{X}) = \) [Input box]
- \( P(68 \le \bar{X} \le 72) = \) [Input box]
---
### (c)
Using the \(\mu_i\) s and \(\sigma_i\) s given in part (a), calculate \( P(-12 \le X_1 - 0.5X_2 - 0.5X_3 \le 6) \).
\[ P(-12 \le X_1 - 0.5X_2 - 0.5X_3 \le 6) = \] [Input box]
#### Interpret the quantity \( X_1 - 0.5X_2 - 0.5X_3 \).
- [ ] The quantity represents the probability that the difference between \( X_3 \) and the sum of \( X_1 \) and \( X_2 \) is between \(-12\)
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