To use the Empirical Rule (68-95-99.7 rule) for a normally distributed set of scores:

1. Scores higher than 78:

   • Mean = 78. Half the scores are above the mean, so:
   • 700 / 2 = 350 students.

2. Scores between 69 and 87:

   • 69 is one standard deviation below the mean (78 - 9 = 69).
   • 87 is one standard deviation above the mean (78 + 9 = 87).
   • According to the Empirical Rule, approximately 68% of scores fall within one standard deviation:
   • 0.68 × 700 ≈ 476 students.

3. Scores between 60 and 96:

   • 60 is two standard deviations below the mean (78 - 18 = 60).
   • 96 is two standard deviations above the mean (78 + 18 = 96).
   • About 95% of scores fall within two standard deviations:
   • 0.95 × 700 ≈ 665 students.

4. Scores between 78 and 87:

   • This is half of the scores from one standard deviation above the mean (from 78 to 87), which is 34% of the distribution:
   • 0.34 × 700 ≈ 238 students.

5. Scores lower than 69:

   • Since 69 is one standard deviation below the mean, about 16% of students score below it:
   • 0.16 × 700 ≈ 112 students.

6. Scores lower than 87:

   • Since 87 is one standard deviation above the mean, about 84% of students score below it:
   • 0.84 × 700 ≈ 588 students.

Summary:

1. Higher than 78: 350 students
2. Between 69 and 87: 476 students
3. Between 60 and 96: 665 students
4. Between 78 and 87: 238 students
5. Lower than 69: 112 students
6. Lower than 87: 588 students

Would you like further details or clarification on any of these points? Here are some related questions you might consider:

1. How does changing the mean or standard deviation affect the distribution?
2. What are the implications of a non-normal distribution?
3. How can you visualize this data with a graph?
4. What percentiles correspond to these scores?
5. How does the Empirical Rule compare with other statistical measures?

Tip: Always verify whether a dataset approximates normality before applying the Empirical Rule.