Find the area of the indicated region under the standard normal curve. -1.6-0.6

To find the area under the standard normal curve between \( z = -1.6 \) and \( z = -0.6 \), we need to use the cumulative distribution function (CDF) of the standard normal distribution, which provides the area to the left of any given \( z \)-value.

### Steps:
1. **Find the area to the left of \( z = -1.6 \)** using the standard normal table (or a calculator with the normal distribution function):
   \[
   P(Z < -1.6) \approx 0.0548
   \]
2. **Find the area to the left of \( z = -0.6 \)**:
   \[
   P(Z < -0.6) \approx 0.2743
   \]
3. **Calculate the area between \( z = -1.6 \) and \( z = -0.6 \)** by subtracting the two areas:
   \[
   \text{Area} = P(Z < -0.6) - P(Z < -1.6) = 0.2743 - 0.0548 = 0.2195
   \]

Thus, the area under the standard normal curve between \( z = -1.6 \) and \( z = -0.6 \) is approximately **0.2195**.

Would you like further details on any part of this calculation?

Here are 5 related questions to explore:
1. How can you calculate the area under the normal curve for any range?
2. What is the significance of a standard normal distribution in statistics?
3. How can technology (calculators, software) simplify finding areas under normal curves?
4. What are \( z \)-scores, and why are they important in standard normal distributions?
5. How do we interpret the area under the curve in real-world contexts?

**Tip:** When using the standard normal table, remember that it provides the cumulative probability from \( -\infty \) to the \( z \)-value.

Find the area of the indicated region under the standard normal curve. -1.6 to -0.6

Learn how to find the area under the standard normal curve between z = -1.6 and z = -0.6 using cumulative distribution function calculations. This problem covers statistical concepts such as probability, standard normal distribution, and the use of z-scores. Suitable for students in Grades 10-12.

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