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### Problem Statement:
Find the probabilities for each of the following given and convert into percentage form.

**GIVEN:**
1. \( P(Z < 1.04) \)
2. \( P(Z \leq -0.5) \)
3. \( P(Z > -1.65) \)
4. \( P(-0.87 < Z \leq 1.31 >) \)
5. \( P(-0.52 < Z < 1.33) \)

I will now solve these problems using the Z-table and then convert them to percentages.

Let me calculate them for you.Here are the probabilities converted into percentage form:

1. \( P(Z < 1.04) \) = **85.08%**
2. \( P(Z \leq -0.5) \) = **30.85%**
3. \( P(Z > -1.65) \) = **95.05%**
4. \( P(-0.87 < Z \leq 1.31) \) = **71.28%**
5. \( P(-0.52 < Z < 1.33) \) = **60.67%**

Would you like more details on how these were calculated or do you have any other questions?

Here are 5 relative questions to expand on this topic:
1. How are Z-scores calculated from raw data in a normal distribution?
2. What is the importance of the standard normal distribution in statistics?
3. How would you calculate the probability for a Z-value not found in a Z-table?
4. What is the difference between \( P(Z \leq z) \) and \( P(Z < z) \)?
5. Can you explain why the total area under the standard normal curve equals 1?

**Tip**: When working with Z-scores, remember that they represent the number of standard deviations away from the mean, making them useful for comparing different data sets.

Find the probabilities for each of the following values and convert them into percentage form: 1) P(Z < 1.04) 2) P(Z <= -0.5) 3) P(Z > -1.65) 4) P(-0.87 < Z <= 1.31) 5) P(-0.52 < Z < 1.33)

Find the probabilities for Z-scores in a standard normal distribution. This detailed guide covers how to calculate probabilities for values such as P(Z < 1.04) and P(Z > -1.65), using the Z-table and converting results into percentage form. Suitable for students in Grades 10-12.

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