To find the percentage of scores that fall within the range of 36 to 64, we can apply the Empirical Rule (also known as the 68-95-99.7 rule), which works for data that is approximately normally distributed. According to this rule:

1. 68% of the data lies within 1 standard deviation of the mean.
2. 95% of the data lies within 2 standard deviations of the mean.
3. 99.7% of the data lies within 3 standard deviations of the mean.

Given:

• Mean ($\mu$) = 50
• Standard deviation ($\sigma$) = 7

Let's calculate the boundaries in terms of standard deviations:

1. Lower boundary: $36 = 50 - 2 \times 7$ (2 standard deviations below the mean)
2. Upper boundary: $64 = 50 + 2 \times 7$ (2 standard deviations above the mean)

Since 36 and 64 represent two standard deviations below and above the mean, respectively, 95% of the scores fall within this range (from 36 to 64).

Thus, approximately 95% of the scores fall within the range of 36 to 64.

Would you like more details or have any questions about this solution?

Here are some additional questions to deepen understanding:

1. What is the Empirical Rule and when can it be applied?
2. How do we determine if a dataset is approximately normally distributed?
3. What percentage of scores fall within 1 standard deviation of the mean in a normal distribution?
4. How does standard deviation affect the spread of scores around the mean?
5. How would we calculate the percentage of scores within a custom range using a standard normal table?

Tip: The Empirical Rule is very useful for quick estimates on normally distributed data. For more precise results, especially with skewed data, using z-scores or statistical software is recommended.