https://file.aiquickdraw.com/mathbot/file/1729490951154gf9cv5y8.jpg

To solve this problem, you are asked to find the probability for a standard normal distribution where:

\[
P(z > 0.07)
\]

### Steps to solve:

1. **Standard Normal Distribution**: This refers to a normal distribution with a mean of 0 and a standard deviation of 1.

2. **Find the z-value**: The z-value here is 0.07. We need to calculate the probability that \( z > 0.07 \).

3. **Use the z-table or a calculator**: A z-table provides the probability that \( z \) is less than a particular value. To get \( P(z > 0.07) \), we first find \( P(z < 0.07) \) from the z-table, then subtract that value from 1.

4. **Look up \( P(z < 0.07) \)** in the standard normal table. For \( z = 0.07 \), the value is approximately **0.5279**.

5. **Calculate \( P(z > 0.07) \)**:
\[
P(z > 0.07) = 1 - P(z < 0.07) = 1 - 0.5279 = 0.4721
\]

So, the probability \( P(z > 0.07) \) is approximately **0.4721** when rounded to 4 decimal places.

Would you like further details or have any questions?

### Related Questions:
1. What is the probability for \( P(z > 1.5) \)?
2. How do you calculate \( P(z < -0.5) \) in a standard normal distribution?
3. What does a negative z-value represent in a standard normal distribution?
4. How would you find \( P(z > 2.5) \)?
5. Can you explain why the total area under a standard normal curve is 1?

**Tip**: When solving problems with a standard normal distribution, always remember that the total probability adds up to 1, and use symmetry of the curve when calculating probabilities for negative z-values.

For a standard normal distribution, find: P(z > 0.07) Express the probability as a decimal rounded to 4 decimal places.

Learn how to calculate the probability P(z > 0.07) for a standard normal distribution. The solution involves using the z-table and basic properties of the normal distribution curve. Suitable for students in Grades 11-12 or introductory college statistics.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation