Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. The area to the right of the z score is .8962

To find the z-score corresponding to an area of 0.8962 to the right of it in a standard normal distribution (mean = 0, standard deviation = 1), we follow these steps:

### Step-by-step process:

1. **Find the area to the left of the z-score**: 
   Since the total area under the curve is 1, the area to the left of the z-score will be:
   
   \[
   \text{Area to the left} = 1 - 0.8962 = 0.1038
   \]

2. **Use the standard normal (Z) table**:
   Using a Z-table or a standard normal distribution calculator, we look for the z-score that corresponds to a cumulative area of 0.1038 to the left.

3. **Find the z-score**: 
   From the Z-table, the z-score that corresponds to a cumulative area of 0.1038 is approximately **-1.26**.

### Answer:
The z-score is **-1.26**.

Would you like more details on how to use the Z-table or have any questions?

Here are 5 related questions to further your understanding:
1. How do you interpret a z-score in the context of a normal distribution?
2. How do you find the area to the right of a given z-score?
3. How does changing the mean and standard deviation affect the z-score?
4. What does it mean when a z-score is negative?
5. How can you find the z-score for a given probability using a calculator?

**Tip**: Remember that a z-score represents how many standard deviations a value is from the mean in a standard normal distribution.

Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. The area to the right of the z score is 0.8962.

Learn how to find the z-score for a given area (0.8962) to the right in a standard normal distribution with mean 0 and standard deviation 1. This step-by-step guide covers core statistical concepts like the z-score and the use of cumulative distribution tables. Suitable for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation