To find the probability \( P(1.25 < z < 2.54) \), we need to refer to the standard normal distribution (Z-distribution). The process is as follows:

### Steps:
1. **Find the cumulative probability for \( z = 2.54 \)** using the Z-table or a calculator:
   \[
   P(Z < 2.54) \approx 0.9945
   \]

2. **Find the cumulative probability for \( z = 1.25 \)** using the Z-table or a calculator:
   \[
   P(Z < 1.25) \approx 0.8944
   \]

3. **Subtract the two probabilities**:
   \[
   P(1.25 < Z < 2.54) = P(Z < 2.54) - P(Z < 1.25)
   \]
   \[
   P(1.25 < Z < 2.54) = 0.9945 - 0.8944 = 0.1001
   \]

Thus, \( P(1.25 < Z < 2.54) \approx 0.1001 \).

Would you like further details or have any questions?

Here are 5 related questions:
1. How do you find probabilities for a standard normal distribution outside the Z-table range?
2. What is the meaning of the Z-score in a standard normal distribution?
3. How do you calculate probabilities for negative Z-scores?
4. Can we use technology (e.g., calculators or software) for cumulative probabilities in normal distributions?
5. How can you standardize a raw score to find its corresponding Z-score?

**Tip**: To solve for normal distribution probabilities, always remember that the total area under the curve is 1. This helps in verifying probabilities.

Learn how to calculate the probability for Z-scores between 1.25 and 2.54 using the standard normal distribution. This solution covers the step-by-step process, including finding cumulative probabilities from a Z-table. Suitable for high school students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation