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To solve the problem \( P(-0.1 < z < 0.84) \) for a standard normal distribution, we need to compute the cumulative probabilities corresponding to these z-values.

1. **Find the cumulative probability for \( z = 0.84 \)**:
   Using the standard normal distribution table (Z-table), or a calculator, the cumulative probability for \( z = 0.84 \) is approximately:
   \[
   P(z \leq 0.84) \approx 0.7995
   \]

2. **Find the cumulative probability for \( z = -0.1 \)**:
   Similarly, the cumulative probability for \( z = -0.1 \) is:
   \[
   P(z \leq -0.1) \approx 0.4602
   \]

3. **Subtract the two cumulative probabilities**:
   To find the probability that \( z \) lies between -0.1 and 0.84, subtract the cumulative probability for \( z = -0.1 \) from the cumulative probability for \( z = 0.84 \):
   \[
   P(-0.1 < z < 0.84) = P(z \leq 0.84) - P(z \leq -0.1)
   \]
   \[
   P(-0.1 < z < 0.84) \approx 0.7995 - 0.4602 = 0.3393
   \]

Thus, the probability \( P(-0.1 < z < 0.84) \) is approximately **0.3393**.

Would you like more details or explanations?

Here are 5 related questions for further exploration:
1. What is the probability that \( z \) is greater than 0.84 in a standard normal distribution?
2. How would you find \( P(z < -0.1) \) in this scenario?
3. What is the total area under the standard normal curve?
4. How do you interpret probabilities in the context of a normal distribution?
5. How can this result be used in hypothesis testing?

**Tip:** For quick standard normal distribution calculations, many scientific calculators have built-in functions that can compute the cumulative distribution function (CDF) values directly.

For a standard normal distribution, find: P(-0.1 < z < 0.84)

Learn how to calculate the probability P(-0.1 < z < 0.84) for a standard normal distribution. This step-by-step solution explains key concepts such as Z-scores, cumulative distribution function (CDF), and the use of Z-tables. Suitable for high school and undergraduate students.

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