Question

1. what percentage of data that is ±2 standard deviations from the mean using the empirical rule. options: 68%, 95%, 99.7%, 97.2%, clear all

Explanation:

Step1: Recall the empirical rule

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

• Approximately \(68\%\) of the data lies within \(\pm1\) standard deviation from the mean.
• Approximately \(95\%\) of the data lies within \(\pm2\) standard deviation from the mean.
• Approximately \(99.7\%\) of the data lies within \(\pm3\) standard deviation from the mean.

Step2: Identify the correct percentage

We are asked for the percentage of data that is \(\pm2\) standard deviations from the mean. From the empirical rule, we know this percentage is \(95\%\).

Answer:

95% (corresponding to the option with "95%")