*Z* is the standard normal variable. Find the indicated probability. (Round your answer to four decimal places.)

*P*(0 ≤ *Z* ≤ 0.6)

To find the probability \( P(0 \leq Z \leq 0.6) \) for a standard normal variable \( Z \), follow these steps:

### Step 1: Look up cumulative probabilities in the **Z-table**.  
The Z-table provides the cumulative probability \( P(Z \leq z) \) from the leftmost tail to a given Z-value.  

- **P(Z ≤ 0)**: Since the Z-table is symmetric, \( P(Z \leq 0) = 0.5 \).
- **P(Z ≤ 0.6)**: From the Z-table, the value for \( Z = 0.6 \) is **0.7257**.

### Step 2: Calculate \( P(0 \leq Z \leq 0.6) \).  
Since \( P(0 \leq Z \leq 0.6) \) is the area between \( Z = 0 \) and \( Z = 0.6 \), we subtract:

\[
P(0 \leq Z \leq 0.6) = P(Z \leq 0.6) - P(Z \leq 0)
\]

\[
P(0 \leq Z \leq 0.6) = 0.7257 - 0.5000 = 0.2257
\]

### Final Answer:
\[
P(0 \leq Z \leq 0.6) = 0.2257
\]

Would you like further explanation on using Z-tables, or do you have additional questions?

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Here are 5 related questions:
1. What is the probability for \( P(Z \geq 1.2) \)?
2. How do you compute \( P(-1 \leq Z \leq 1) \)?
3. What is the total area under the standard normal curve?
4. How can we use the Z-table to find \( P(Z \leq -0.8) \)?
5. How does symmetry help when computing probabilities for Z-values around 0?

**Tip:** Always subtract cumulative probabilities carefully to avoid calculation errors when finding areas between two Z-values.

Z is the standard normal variable. Find the indicated probability. (Round your answer to four decimal places.) P(0 ≤ Z ≤ 0.6)

Learn how to calculate the probability P(0 ≤ Z ≤ 0.6) for a standard normal variable Z. This problem involves using Z-tables, calculating cumulative probabilities, and understanding the properties of the standard normal distribution. Suitable for students in Grades 10-12.

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