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

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.
Expert Solution

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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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Follow-up Question
![**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.*](https://content.bartleby.com/qna-images/question/ac3be618-b645-4bd8-855b-808ff3fc18d4/f3b2e266-adfa-4ce8-8ef8-6b45ab343ab4/57cgoyq_thumbnail.png)
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.*
Solution
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