MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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### Finding Probability for the Standard Normal Distribution

To find the probability of \( p(1.28 < z < 2.28) \) for the standard normal distribution, we consult the cumulative standard normal distribution table (Table E). 

**Step-by-Step Guide:**

1. **Locate the cumulative probability for \( z = 1.28 \):**
   - Navigate through the rows of the table to find the value at 1.2.
   - Move horizontally to the column under 0.08. The intersection gives us the cumulative probability.

   **Result:**
   \( P(Z \leq 1.28) = 0.8997 \)

2. **Locate the cumulative probability for \( z = 2.28 \):**
   - Again, find the row for 2.2.
   - Move horizontally to the column under 0.08.

   **Result:**
   \( P(Z \leq 2.28) = 0.9887 \)

3. **Calculate the desired probability:**
   - Subtract the cumulative probability at \( z = 1.28 \) from the cumulative probability at \( z = 2.28 \).

   **Calculation:**
   \( P(1.28 < Z < 2.28) = P(Z \leq 2.28) - P(Z \leq 1.28) \)
   \( P(1.28 < Z < 2.28) = 0.9887 - 0.8997 = 0.0890 \)

**Answer:**
\[ p(1.28 < z < 2.28) = 0.0890 \]

### Explanation of the Standard Normal Distribution Table:

The table provided displays values for the cumulative standard normal distribution. The values indicate the probability that a standard normal variable (z) will have a value less than or equal to a given z-score. The table is structured as follows:

- **Row labels (first column):** Represent the integer and first decimal place of the z-score.
- **Column labels:** Represent the second decimal place of the z-score.
- **Cell values:** Indicate the cumulative probability up to that z-score.

For example:
- **Intersection of row 1.2 and column 0.08:** Indicates the cumulative probability for \( z = 1.28 \).
- **Intersection of row 2
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Transcribed Image Text:### Finding Probability for the Standard Normal Distribution To find the probability of \( p(1.28 < z < 2.28) \) for the standard normal distribution, we consult the cumulative standard normal distribution table (Table E). **Step-by-Step Guide:** 1. **Locate the cumulative probability for \( z = 1.28 \):** - Navigate through the rows of the table to find the value at 1.2. - Move horizontally to the column under 0.08. The intersection gives us the cumulative probability. **Result:** \( P(Z \leq 1.28) = 0.8997 \) 2. **Locate the cumulative probability for \( z = 2.28 \):** - Again, find the row for 2.2. - Move horizontally to the column under 0.08. **Result:** \( P(Z \leq 2.28) = 0.9887 \) 3. **Calculate the desired probability:** - Subtract the cumulative probability at \( z = 1.28 \) from the cumulative probability at \( z = 2.28 \). **Calculation:** \( P(1.28 < Z < 2.28) = P(Z \leq 2.28) - P(Z \leq 1.28) \) \( P(1.28 < Z < 2.28) = 0.9887 - 0.8997 = 0.0890 \) **Answer:** \[ p(1.28 < z < 2.28) = 0.0890 \] ### Explanation of the Standard Normal Distribution Table: The table provided displays values for the cumulative standard normal distribution. The values indicate the probability that a standard normal variable (z) will have a value less than or equal to a given z-score. The table is structured as follows: - **Row labels (first column):** Represent the integer and first decimal place of the z-score. - **Column labels:** Represent the second decimal place of the z-score. - **Cell values:** Indicate the cumulative probability up to that z-score. For example: - **Intersection of row 1.2 and column 0.08:** Indicates the cumulative probability for \( z = 1.28 \). - **Intersection of row 2
**Quiz Question Options:**

The following are the possible answers for the quiz question: 

- ( ) 1.0000
- ( ) -1.0000
- ( ) 0.0890
- ( ) 0.9887

Please select the correct answer by clicking on the corresponding radio button.
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Transcribed Image Text:**Quiz Question Options:** The following are the possible answers for the quiz question: - ( ) 1.0000 - ( ) -1.0000 - ( ) 0.0890 - ( ) 0.9887 Please select the correct answer by clicking on the corresponding radio button.
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