calculate percentage for z score of +0.78 % below this z score in the body

To find the percentage of data below a Z-score of +0.78, we use the standard normal distribution table or a calculator.

1. **Find the cumulative probability** for the Z-score of +0.78. This gives us the proportion of the data below this Z-score.

Using the Z-table or a standard normal distribution calculator:
- The cumulative probability for a Z-score of +0.78 is approximately **0.7823**.

2. **Convert to a percentage**:
\[ 0.7823 \times 100 = 78.23\% \]

So, approximately **78.23%** of the data falls below a Z-score of +0.78.

Would you like further details or have any other questions?

### Related Questions:
1. What is the percentage of data above a Z-score of +0.78?
2. How do you calculate the Z-score for a given value in a data set?
3. What is the probability for a Z-score of -0.78?
4. How can you use Z-scores to compare two different data sets?
5. How is the standard normal distribution used in hypothesis testing?

### Tip:
When using a Z-table, remember that it provides the cumulative probability from the mean up to the Z-score value for positive Z-scores and from the Z-score down for negative values.

Learn how to calculate the percentage of data below a Z-score of +0.78 using the standard normal distribution. This tutorial covers the conversion of Z-scores to cumulative probabilities with step-by-step solutions. Suitable for high school statistics students (Grades 10-12).

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