Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. Click to view page 1 of the table. Click to view page 2 of the table. 0.9871 The indicated z score is (Round to two decimal places as needed.)
Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. Click to view page 1 of the table. Click to view page 2 of the table. 0.9871 The indicated z score is (Round to two decimal places as needed.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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 [Click to view page 2 of the table.](#)
**Visual Explanation:**
The graph provided illustrates the standard normal distribution, which is a bell-shaped curve characterized by a mean (μ) of 0 and a standard deviation (σ) of 1.
- The area under the curve to the left of a certain z-value is given as 0.9871.
**Objective:** Determine the z-score corresponding to this given cumulative area.
**Solution Steps:**
1. **Check the Cumulative Area:** The total area under a standard normal curve is 1.0. The given area (0.9871) represents the cumulative probability from the left tail of the distribution up to a particular z-value.
2. **Use the Standard Normal Table:** To find the z-score, consult the standard normal (z) table which shows the cumulative area for different z-values.
3. **Find Closest Area:**
- Look through the z-table to find the closest area to 0.9871.
- Typically, tables are organized with z-values listed in including rows and columns. Using these, locate the value closest to 0.9871.
4. **Derive the z-Score:**
- The z-score is the value on the row and column intersection that corresponds to an area closest to 0.9871.
5. **Accuracy Check:** Ensure the z-score is accurate, generally rounded to two decimal places as required.
**Conclusion:**
**The indicated z-score is:**
\[ \boxed{} \]
(Round to two decimal places as needed.)
By understanding the process of finding a z-score using the standard normal table and correlating it with the cumulative area under the curve, you can accurately interpret values in a standard normal distribution.
**Graph Description:**
The graph provided in the example problem is a standard normal distribution curve. It features:
- A symmetrical bell-shaped curve centered at a mean of 0 (the highest point).
- The z-axis at the horizontal base.
- The cumulative area shaded from the left tail up to the point where the z-value is being sought.
- The given area under the](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F15c363dd-bee0-4851-8a57-e357b273329c%2Fdc863816-c033-40cc-8f91-2a7a1bb9d6f2%2F4f0f12c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Topic: Understanding Z-Scores in Standard Normal Distribution
**Example Problem:**
**Task:** Find the indicated z-score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.
**Instructions:**
[Click to view page 1 of the table.](#) [Click to view page 2 of the table.](#)
**Visual Explanation:**
The graph provided illustrates the standard normal distribution, which is a bell-shaped curve characterized by a mean (μ) of 0 and a standard deviation (σ) of 1.
- The area under the curve to the left of a certain z-value is given as 0.9871.
**Objective:** Determine the z-score corresponding to this given cumulative area.
**Solution Steps:**
1. **Check the Cumulative Area:** The total area under a standard normal curve is 1.0. The given area (0.9871) represents the cumulative probability from the left tail of the distribution up to a particular z-value.
2. **Use the Standard Normal Table:** To find the z-score, consult the standard normal (z) table which shows the cumulative area for different z-values.
3. **Find Closest Area:**
- Look through the z-table to find the closest area to 0.9871.
- Typically, tables are organized with z-values listed in including rows and columns. Using these, locate the value closest to 0.9871.
4. **Derive the z-Score:**
- The z-score is the value on the row and column intersection that corresponds to an area closest to 0.9871.
5. **Accuracy Check:** Ensure the z-score is accurate, generally rounded to two decimal places as required.
**Conclusion:**
**The indicated z-score is:**
\[ \boxed{} \]
(Round to two decimal places as needed.)
By understanding the process of finding a z-score using the standard normal table and correlating it with the cumulative area under the curve, you can accurately interpret values in a standard normal distribution.
**Graph Description:**
The graph provided in the example problem is a standard normal distribution curve. It features:
- A symmetrical bell-shaped curve centered at a mean of 0 (the highest point).
- The z-axis at the horizontal base.
- The cumulative area shaded from the left tail up to the point where the z-value is being sought.
- The given area under the
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