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Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.
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z equals 0.79

A normal curve is over a horizontal axis. A vertical line segment labeled z = 0.79 extends from the horizontal axis to the curve at 0.79. The area under the curve and to the left of the vertical line segment is shaded.
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Part 1
The area of the shaded region is

enter your response here.
​(Round to four decimal places as​ needed.)

To find the area of the shaded region, we need to look up the z-score \( z = 0.79 \) in the standard normal distribution table. This will give us the cumulative area to the left of \( z = 0.79 \).

Let's proceed with these steps:

1. **Locate the z-score**: A z-score of 0.79 is used, so we need the cumulative area for this value.
2. **Use the z-score table**: The area associated with \( z = 0.79 \) in the standard normal table corresponds to the probability that a random variable \( Z \) is less than 0.79.

Looking up \( z = 0.79 \) in the table, we find:

\[
P(Z < 0.79) \approx 0.7852
\]

Thus, the area of the shaded region is approximately **0.7852**.

### Would you like a detailed explanation on how to use the z-score table or any other aspect of this problem?

### Related Questions:
1. What if the z-score was negative, e.g., \( z = -0.79 \)?
2. How do you calculate the area to the right of \( z = 0.79 \)?
3. What is the interpretation of the area under the standard normal curve?
4. How does changing the standard deviation affect the shape of the normal distribution?
5. What are the properties of the standard normal distribution?

### Tip:
When using the z-score table, remember that it provides the area to the left of the given z-score. For the area to the right, you simply subtract the given area from 1.

Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. The z-score is 0.79. Round to four decimal places as needed.

Learn how to find the area of the shaded region under a standard normal distribution curve for z = 0.79. This problem covers essential statistical concepts, including z-scores, probability, and cumulative area calculations. Suitable for students in Grades 10-12.

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