How much data lies between ± 2σ of the standard deviation of the mean? 93% 95% 95.5% 96.1%

1. ### Break Down the Problem

To determine the percentage of data that lies within ±2σ (two standard deviations) of the mean in a normal distribution, we need to identify the correct value from the options provided: 93%, 95%, 95.5%, 96.1%.

2. ### Relevant Concepts

In statistics, according to the empirical rule (or 68-95-99.7 rule) for normal distributions:

• Approximately 68% of the data falls within ±1σ of the mean.
• Approximately 95% of the data falls within ±2σ of the mean.
• Approximately 99.7% of the data falls within ±3σ of the mean.

3. ### Analysis and Detail

Given that we are looking for the data within ±2σ:

• From the empirical rule, it is established that roughly 95% of the data in a normal distribution will fall within two standard deviations from the mean.

4. ### Verify and Summarize

We have applied the empirical rule correctly to our problem. The other percentages are incorrect based on the empirical rule context for a normal distribution.

Final Answer

The percentage of data that lies between ±2σ of the standard deviation of the mean is 95%.