Q9.2 VPlease answer d, e, and f. **Title: Probability Calculations Using Standard Normal Random Variables****Objective:**Let \( Z \) be a standard normal random variable and calculate the following probabilities, drawing pictures wherever appropriate. (Round your answers to four decimal places.)**Problems:**(a) \( P(0 \leq Z \leq 2.41) \)- Input box for solution.(b) \( P(0 \leq Z \leq 2) \)- Input box for solution.(c) \( P(-2.10 \leq Z \leq 0) \)- Input box for solution.(d) \( P(-2.10 \leq Z \leq 2.10) \)- Input box for solution.(e) \( P(Z \leq 1.06) \)- Input box for solution.(f) \( P(-1.25 \leq Z) \)- Input box for solution.**Instructions:**To calculate each probability, you can use standard normal distribution tables (z-tables) or statistical software. For visual tasks, you may sketch the areas under the standard normal curve corresponding to each probability range.**Note:** Make sure you round your final answers to four decimal places.**Example Diagram Explanation:**For part (a), \( P(0 \leq Z \leq 2.41) \), you should shade the area under the curve from \( Z = 0 \) to \( Z = 2.41 \). The same procedure should be followed for other parts where you shade the areas under the curve corresponding to the specified ranges of \( Z \).**Interactive Tool:**Use the button labeled **"USE SALT"** to assist in calculations or visualizations where necessary.---By following these guidelines and utilizing the provided tools, you will be able to accurately compute and visualize the required probabilities for a standard normal random variable.

As per our guidelines we can solve given three sub part (d, e, and f) of question and rest can be…

Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures wherever appropriate. (Round your answers to four decimal places.) USE SALT (a) P(0 ≤ Z ≤ 2.41) (b) P(0 ≤Z≤ 2) (c) P(-2.10 ≤ Z ≤ 0) (d) P(-2.10 ≤ Z ≤ 2.10) (e) P(Z ≤ 1.06) (f) P(-1.25 ≤ Z)

Let Z be a standard normal random variable and calculate the following probabilities, drawing pictures wherever appropriate. (Round your answers to four decimal places.) USE SALT (a) P(0 ≤ Z ≤ 2.41) (b) P(0 ≤Z≤ 2) (c) P(-2.10 ≤ Z ≤ 0) (d) P(-2.10 ≤ Z ≤ 2.10) (e) P(Z ≤ 1.06) (f) P(-1.25 ≤ Z)

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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Question

Q9.2 VPlease answer d, e, and f.

**Title: Probability Calculations Using Standard Normal Random Variables**

**Objective:**
Let \( Z \) be a standard normal random variable and calculate the following probabilities, drawing pictures wherever appropriate. (Round your answers to four decimal places.)

**Problems:**

(a) \( P(0 \leq Z \leq 2.41) \)
- Input box for solution.

(b) \( P(0 \leq Z \leq 2) \)
- Input box for solution.

(c) \( P(-2.10 \leq Z \leq 0) \)
- Input box for solution.

(d) \( P(-2.10 \leq Z \leq 2.10) \)
- Input box for solution.

(e) \( P(Z \leq 1.06) \)
- Input box for solution.

(f) \( P(-1.25 \leq Z) \)
- Input box for solution.

**Instructions:**

To calculate each probability, you can use standard normal distribution tables (z-tables) or statistical software. For visual tasks, you may sketch the areas under the standard normal curve corresponding to each probability range.

**Note:** Make sure you round your final answers to four decimal places.

**Example Diagram Explanation:**

For part (a), \( P(0 \leq Z \leq 2.41) \), you should shade the area under the curve from \( Z = 0 \) to \( Z = 2.41 \). The same procedure should be followed for other parts where you shade the areas under the curve corresponding to the specified ranges of \( Z \).

**Interactive Tool:**

Use the button labeled **"USE SALT"** to assist in calculations or visualizations where necessary.

---

By following these guidelines and utilizing the provided tools, you will be able to accurately compute and visualize the required probabilities for a standard normal random variable.

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