https://file.aiquickdraw.com/mathbot/file/1728181119020c5kmo7wy.jpg

This problem involves finding the area of the shaded region under the standard normal distribution curve, which is a bell-shaped curve with a mean of 0 and a standard deviation of 1.

The shaded region lies between two z-scores: \( z = -2.36 \) and \( z = -1.18 \).

To find the area of this shaded region, we can use the cumulative distribution function (CDF) for the standard normal distribution. The steps are as follows:

1. **Find the cumulative probability for \( z = -1.18 \)** (which gives the area to the left of this z-score).
2. **Find the cumulative probability for \( z = -2.36 \)** (which gives the area to the left of this z-score).
3. **Subtract the second probability from the first** to get the area between \( z = -2.36 \) and \( z = -1.18 \).

### Using Standard Normal Table or Calculator:
- The cumulative probability for \( z = -1.18 \) is approximately \( 0.1190 \).
- The cumulative probability for \( z = -2.36 \) is approximately \( 0.0091 \).

### Calculate the area:
\[
\text{Area} = P(z = -1.18) - P(z = -2.36) = 0.1190 - 0.0091 = 0.1099
\]

So, the area of the shaded region is approximately **0.1099**.

Would you like more details or further clarification?

Here are 5 related questions for further study:
1. How do you calculate the z-score for a given data point?
2. What is the significance of the area under the normal curve in probability theory?
3. How can you calculate areas for non-standard normal distributions?
4. What is the difference between the z-distribution and t-distribution?
5. How is the standard normal distribution used in hypothesis testing?

**Tip:** When using a standard normal table, remember that it gives the cumulative probability from the far left of the curve up to the specified z-score.

Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.

Learn how to calculate the area between the z-scores -2.36 and -1.18 in a standard normal distribution with mean 0 and standard deviation 1. This example shows how to use the cumulative distribution function (CDF) and standard normal tables for probability calculations.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation