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.)---### (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 $-12$

(b). Calculate the values of P(64 ≤ X-bar) and P(68 ≤ X-bar ≤72): Given that X1, X2 and X3 are…

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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Concept explainers

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Question

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.)

---

### (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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