In a normal distribution, what percentage of the data falls within 3 standard deviations of the mean?A.99.7%B.34%C.95%D.68%SUBMITarrow_backPREVIOUS

1. Break Down the Problem

We need to determine the percentage of data that falls within 3 standard deviations of the mean in a normal distribution.

2. Relevant Concepts

In a normal distribution (bell curve), the empirical rule (or 68-95-99.7 rule) states:

• 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.

3. Analysis and Detail

According to the empirical rule:

• For 3 standard deviations:
  • This means we are looking at values from $\mu - 3\sigma$ to $\mu + 3\sigma$, where $\mu$ represents the mean and $\sigma$ represents the standard deviation.

4. Verify and Summarize

Since this is a known statistical rule, we confirm that the percentage of data within 3 standard deviations of the mean is indeed 99.7%.

Final Answer

A. 99.7%