A normal distribution has a mean of 15 and a standard deviation of 3. What interval contains approximately 95% of the data, according to the Empirical Rule?

This problem uses the Empirical Rule (also known as the 68-95-99.7 rule) for normal distributions. This 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.

We are given:

• Mean ($\mu$) = 15
• Standard deviation ($\sigma$) = 3

We need to find the interval that includes about 95% of the probability. According to the Empirical Rule, this interval is $\mu \pm 2\sigma$.