Calculate the probability of the following using only the z-table (Express your answers in percentage with 2 decimal places. Ex: 4.00%)


P (z ≥ 2.1) =

To calculate the probability \( P(z \geq 2.1) \) using the z-table, follow these steps:

1. **Find the z-score on the z-table:**
   - The z-table provides the area to the left of the z-score. First, find the value corresponding to \( z = 2.1 \) in the z-table.
   - The z-table value for \( z = 2.1 \) is approximately \( 0.9821 \).

2. **Convert this to the area to the right:**
   - Since the z-table gives the area to the left, and we need \( P(z \geq 2.1) \), which is the area to the right, subtract the table value from 1.
   - \( P(z \geq 2.1) = 1 - 0.9821 = 0.0179 \).

3. **Convert the decimal to a percentage:**
   - \( 0.0179 \times 100\% = 1.79\% \).

Thus, the probability \( P(z \geq 2.1) \) is **1.79%**.

Would you like more details or have any questions?

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**Relative Questions:**

1. How would you calculate \( P(z \leq 2.1) \) using the z-table?
2. What is the probability \( P(-2.1 \leq z \leq 2.1) \)?
3. How would you calculate \( P(z \geq -2.1) \)?
4. What is the probability \( P(z \geq 1.5) \)?
5. How do you interpret a very small probability like \( P(z \geq 2.1) \) in a real-world scenario?
6. What does the z-score of 2.1 represent in a normal distribution?
7. How would you find \( P(z \geq -0.5) \) using the z-table?
8. What steps would you take to calculate \( P(z \geq 3.0) \)?

**Tip:** For large positive z-scores, the area to the right becomes small, indicating rare events in a standard normal distribution.

Learn how to calculate the probability P(z ≥ 2.1) using the Z-table with a detailed step-by-step guide. Understand the concept of z-scores and how to interpret them in probability calculations. Suitable for advanced high school and college students.

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