To calculate the probability \( P(z \leq -0.79) \) using the standard normal distribution, we need to refer to the Z-table or use a calculator that computes values for the standard normal distribution.

The Z-table gives the cumulative probability from the far left of the distribution up to a given z-value. A negative z-value represents a point on the left side of the mean (which is 0 in a standard normal distribution).

For \( z = -0.79 \):

1. Look up the value in the Z-table for \( z = -0.79 \), or
2. Use a calculator to find the cumulative probability.

The cumulative probability for \( z = -0.79 \) is approximately **0.2148**.

Thus, 
\[
P(z \leq -0.79) \approx 0.2148
\]

Would you like more details on how to interpret Z-scores or the normal distribution?

Here are 5 related questions to consider:
1. How do you find probabilities for other z-values?
2. What is the meaning of a Z-score in statistics?
3. How do you calculate Z-scores from raw data?
4. What is the difference between one-tailed and two-tailed probabilities?
5. How can you use the Z-table to find probabilities between two values?

**Tip:** Always remember that the total area under the normal distribution curve equals 1 (or 100%).

Learn how to calculate the probability P(z ≤ −0.79) using the Z-table and standard normal distribution. This problem demonstrates the process of finding cumulative probability for negative Z-scores, covering key statistical concepts like Z-scores and the normal distribution. Suitable for students in Grades 10-12.

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