In a normal distribution, 68% of the data falls within 1 standard deviation of the mean.
A. True
B. False

The empirical rule states that approximately 68% of the data in a normal distribution falls within 1 standard deviation of the mean.
The given statement aligns with the empirical rule.
Therefore, the statement is true.
The final answer is: T r u e ​ .

Explanation

Analyze the problem The question states that in a normal distribution, 68% of the data falls within 1 standard deviation of the mean. We need to determine if this statement is true or false.

Recall the empirical rule The empirical rule (also known as the 68-95-99.7 rule) states that for a normal distribution:



Approximately 68% of the data falls within 1 standard deviation of the mean.
Approximately 95% of the data falls within 2 standard deviations of the mean.
Approximately 99.7% of the data falls within 3 standard deviations of the mean.


Compare the statement with the empirical rule Comparing the given statement with the empirical rule, we see that the statement 'In a normal distribution, 68% of the data falls within 1 standard deviation of the mean' is consistent with the empirical rule.

Conclusion Therefore, the statement is true.


Examples
Understanding normal distributions is crucial in many real-world scenarios. For example, in quality control, manufacturers use the 68-95-99.7 rule to determine if the weight of a product is within acceptable limits. If a cereal box is labeled to contain 500 grams, the manufacturer might aim for 68% of the boxes to be within 1 standard deviation of 500 grams, ensuring consistency and customer satisfaction.

Answered by GinnyAnswer | 2025-07-08