Understanding the Problem:
We are given an interval in the form (μ - 30, μ + 30) and we need to determine the percentage of the normal distribution that is covered by this interval.

Solution:
To solve this problem, we need to understand the concept of the normal distribution and its properties.

Normal Distribution:
A normal distribution, also known as a Gaussian distribution, is a probability distribution that is symmetric and bell-shaped. It is characterized by its mean (μ) and standard deviation (σ).

Properties of a Normal Distribution:
1. The total area under a normal distribution curve is equal to 1 or 100%.
2. The mean (μ) of a normal distribution is the center of the distribution and represents the highest point on the curve.
3. The standard deviation (σ) determines the spread or width of the distribution.

Empirical Rule:
The empirical rule, also known as the 68-95-99.7 rule, provides a way to estimate the percentage of data within a certain number of standard deviations from the mean in a normal distribution. According to this rule:
- Approximately 68% of the data falls within one standard deviation of the mean (μ ± σ).
- Approximately 95% of the data falls within two standard deviations of the mean (μ ± 2σ).
- Approximately 99.7% of the data falls within three standard deviations of the mean (μ ± 3σ).

Applying the Empirical Rule:
In our case, the interval is (μ - 30, μ + 30), which means it covers 30 units on both sides of the mean. To determine the percentage of the normal distribution covered by this interval, we need to determine how many standard deviations this interval represents and then apply the empirical rule.

Since the interval covers 30 units on both sides of the mean, it covers a total of 2*30 = 60 units. Since each standard deviation represents 34% of the data according to the empirical rule, we can calculate the number of standard deviations represented by this interval as follows:

Number of standard deviations = 60 / (34% * 2) = 60 / 0.68 ≈ 88.24%

Therefore, the interval (μ - 30, μ + 30) covers approximately 88.24% of the normal distribution.

Answer:
The interval (μ - 30, μ + 30) covers approximately 88.24% of the normal distribution.