(a) Z= -0.42, (b) Z= -1.31, (c) Z= - 1.74, ar

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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The image displays a Standard Normal Distribution Table (Table V), which is used to find the probability that a statistic is observed below, above, or between values on the standard normal distribution. This table provides areas (probabilities) under the curve of a standard normal distribution.

### Structure of the Table:

- **Left Column (z):** 
  - This column represents the z-score, which indicates how many standard deviations an element is from the mean.
  - It ranges from -3.4 to 3.4 in increments of 0.1.

- **Top Row (.00 to .09):** 
  - Indicates the second decimal place of the z-score.
  - Used to refine the z-score to two decimal places.

### How to Use the Table:

1. **Identify the z-score:** 
   - Find the row corresponding to the z-score's integer and first decimal point (e.g., for z = 1.36, look at 1.3).

2. **Locate the precise value:**
   - Follow the row across to the column that matches the hundredths place of your z-score (e.g., if the z-score is 1.36, find the column labeled .06).

3. **Read the probability:**
   - The cell where the row and column intersect gives the probability that a value is less than the z-score.

### Example:

- For a z-score of -1.52:
  - Locate -1.5 in the left column.
  - Move across to the column under .02.
  - The value found is 0.0643, which represents the probability that a score is less than -1.52.

This table is critical for calculating probabilities in various statistics and data analysis applications, helping researchers and students understand data variability and characteristics relative to a normal distribution.
Transcribed Image Text:The image displays a Standard Normal Distribution Table (Table V), which is used to find the probability that a statistic is observed below, above, or between values on the standard normal distribution. This table provides areas (probabilities) under the curve of a standard normal distribution. ### Structure of the Table: - **Left Column (z):** - This column represents the z-score, which indicates how many standard deviations an element is from the mean. - It ranges from -3.4 to 3.4 in increments of 0.1. - **Top Row (.00 to .09):** - Indicates the second decimal place of the z-score. - Used to refine the z-score to two decimal places. ### How to Use the Table: 1. **Identify the z-score:** - Find the row corresponding to the z-score's integer and first decimal point (e.g., for z = 1.36, look at 1.3). 2. **Locate the precise value:** - Follow the row across to the column that matches the hundredths place of your z-score (e.g., if the z-score is 1.36, find the column labeled .06). 3. **Read the probability:** - The cell where the row and column intersect gives the probability that a value is less than the z-score. ### Example: - For a z-score of -1.52: - Locate -1.5 in the left column. - Move across to the column under .02. - The value found is 0.0643, which represents the probability that a score is less than -1.52. This table is critical for calculating probabilities in various statistics and data analysis applications, helping researchers and students understand data variability and characteristics relative to a normal distribution.
**Determine the Area Under the Standard Normal Curve**

The goal is to find the area under the standard normal curve that lies to the left of specific Z-scores:
- (a) Z = -0.42
- (b) Z = -1.31
- (c) Z = -1.74
- (d) Z = -1.22

A clickable icon is available to view a table of areas under the normal curve. This table is useful in determining the cumulative probability for each Z-score.

(a) **Task**: Find the area to the left of Z = -0.42.
- **Instruction**: Round your answer to four decimal places as needed.

**Note**: Use the standard normal distribution table (Z-table) or software tools to find the required cumulative probabilities.
Transcribed Image Text:**Determine the Area Under the Standard Normal Curve** The goal is to find the area under the standard normal curve that lies to the left of specific Z-scores: - (a) Z = -0.42 - (b) Z = -1.31 - (c) Z = -1.74 - (d) Z = -1.22 A clickable icon is available to view a table of areas under the normal curve. This table is useful in determining the cumulative probability for each Z-score. (a) **Task**: Find the area to the left of Z = -0.42. - **Instruction**: Round your answer to four decimal places as needed. **Note**: Use the standard normal distribution table (Z-table) or software tools to find the required cumulative probabilities.
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Determine the area under the standard normal curve that lies to the left of

(a) Z = - 0.42 (b) Z = - 1.31 , (c) Z = - 1.74

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**Determine the area under the standard normal curve that lies to the left of given Z-values:**

(a) Z = -0.42  
- The area to the left is **0.3372**.  
(Round to four decimal places as needed.)

(b) Z = -1.31  
- The area to the left is **0.0951**.  
(Round to four decimal places as needed.)

(c) Z = -1.74  
- The area to the left is **0.0409**.  
(Round to four decimal places as needed.)

(d) Z = -1.22  
- The area to the left is **[box for value]**.  
(Round to four decimal places as needed.)

*Note: Click the icon to view a table of areas under the normal curve for more information.*
Transcribed Image Text:**Determine the area under the standard normal curve that lies to the left of given Z-values:** (a) Z = -0.42 - The area to the left is **0.3372**. (Round to four decimal places as needed.) (b) Z = -1.31 - The area to the left is **0.0951**. (Round to four decimal places as needed.) (c) Z = -1.74 - The area to the left is **0.0409**. (Round to four decimal places as needed.) (d) Z = -1.22 - The area to the left is **[box for value]**. (Round to four decimal places as needed.) *Note: Click the icon to view a table of areas under the normal curve for more information.*
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