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.)

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### 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
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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