A normally distributed data set has a mean of 50 and a standard deviation of 7. Which two values does 68% of the data fall between?






In a normally distributed data set, **68%** of the data falls within **one standard deviation** of the mean. This is a key property of the normal distribution known as the **empirical rule**.

### Given:
- Mean (\(\mu\)) = 50
- Standard deviation (\(\sigma\)) = 7

### Step 1: Calculate the values that are one standard deviation below and above the mean.
- **Lower bound**: Mean - 1 standard deviation
  \[
  50 - 7 = 43
  \]
- **Upper bound**: Mean + 1 standard deviation
  \[
  50 + 7 = 57
  \]

### Answer:
**68% of the data** falls between the values **43 and 57**.

Would you like more details or have any questions?

Here are some related questions to explore:

1. What range of values contains 95% of the data in this distribution?
2. What percentage of data falls between 36 and 50?
3. How would the range change if the standard deviation increased to 10?
4. What is the Z-score for a value of 60 in this distribution?
5. What is the probability of selecting a data point less than 43?

**Tip:** The empirical rule (68-95-99.7 rule) is a quick way to estimate the spread of data in a normal distribution.

Explore how the empirical rule applies to a normally distributed dataset with a mean of 50 and a standard deviation of 7. Learn how to calculate the range where 68% of the data falls. Suitable for advanced high school students.

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