Find the percentage of all values in a normal distribution for the following​ z-score.

z greater than or equals 1.41z≥1.41

To find the percentage of all values in a normal distribution for the given z-score (where \( z \geq 1.41 \)), we can follow a similar approach as before.

### Step 1: Find the cumulative probability for \( z = 1.41 \)
Using the standard normal distribution table or a calculator, we find the cumulative probability (area to the left) for \( z = 1.41 \).

The cumulative probability \( P(Z < 1.41) \) is approximately **0.9207**.

### Step 2: Calculate the area to the right
Since we want the area to the right of \( z = 1.41 \), we subtract the cumulative probability from 1:

\[
P(Z \geq 1.41) = 1 - P(Z < 1.41) = 1 - 0.9207 = 0.0793
\]

### Step 3: Convert to a percentage
To convert this to a percentage, multiply by 100:

\[
P(Z \geq 1.41) = 0.0793 \times 100 = 7.93\%
\]

### Final Answer:
Approximately **7.93%** of the values in a normal distribution have a z-score greater than or equal to 1.41.

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Would you like more details on the standard normal distribution, or do you have any other questions?

Here are 5 related questions you might find interesting:

1. What is the percentage for a z-score less than or equal to 1.41?
2. How do you calculate the percentage for \( z \geq 1.96 \)?
3. Can you find the percentage for a z-score between 1.41 and 2.00?
4. How do you interpret z-scores in terms of standard deviations from the mean?
5. What is the significance of the 50th percentile in a normal distribution?

**Tip:** When using z-tables or calculators, remember that they typically provide the cumulative probability up to the given z-score (area to the left). To find the area to the right, simply subtract this value from 1.

Learn how to calculate the percentage of values in a normal distribution with a z-score greater than or equal to 1.41. Step-by-step solution using cumulative probability and standard normal distribution principles. Suitable for advanced high school students and beyond.

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