For a standard normal distribution, find:

P(-1.99 < z < -0.23)

To find the probability for the standard normal distribution between \( z = -1.99 \) and \( z = -0.23 \), you can use a standard normal table (Z-table) or a calculator. The Z-table gives the cumulative probability from the left of the curve up to a given z-value.

1. **Find the cumulative probability for \( z = -1.99 \):**
   From the Z-table, \( P(Z < -1.99) \approx 0.0233 \).

2. **Find the cumulative probability for \( z = -0.23 \):**
   From the Z-table, \( P(Z < -0.23) \approx 0.4090 \).

3. **Calculate the probability between the two values:**
   \[
   P(-1.99 < Z < -0.23) = P(Z < -0.23) - P(Z < -1.99)
   \]
   \[
   P(-1.99 < Z < -0.23) = 0.4090 - 0.0233 = 0.3857
   \]

So, \( P(-1.99 < Z < -0.23) \approx 0.3857 \).

Would you like more details or have any questions?

### Relative questions:
1. What is the cumulative probability for \( z = 1.99 \)?
2. How do you calculate the probability \( P(Z > z) \) for a given z-value?
3. What is the probability between two positive z-values (e.g., \( P(0.5 < Z < 1.5) \))?
4. How can you calculate probabilities using a calculator instead of a Z-table?
5. How do you interpret z-values in a real-world context (e.g., in height or test scores)?

### Tip:
Always remember that the Z-table typically provides the area to the left of a z-value, so subtracting cumulative probabilities is key for finding the area between two z-values.

For a standard normal distribution, find: P(-1.99 < z < -0.23)

Learn how to find the probability between two z-values, P(-1.99 < z < -0.23), in a standard normal distribution using Z-tables and the cumulative distribution function. Detailed solution with step-by-step instructions, suitable for Grades 11-12 or college students studying probability and statistics.

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