To determine the range within which 68% of the eighth-grade students' scores fall, we follow these steps:
1. Mean and Standard Deviation Identification: The mean (average) score of the students is 57.5, and the standard deviation, which measures the dispersion of the scores around the mean, is 6.5.
2. 68% Rule in Normal Distribution: According to the empirical rule (or 68-95-99.7 rule) for normally distributed data, approximately 68% of the data falls within one standard deviation of the mean.
3. Calculating the Lower Bound: The lower boundary of this range is calculated by subtracting one standard deviation from the mean:
- Mean: 57.5
- Standard Deviation: 6.5
- Lower Bound: 57.5 - 6.5 = 51.0
4. Calculating the Upper Bound: The upper boundary of this range is calculated by adding one standard deviation to the mean:
- Mean: 57.5
- Standard Deviation: 6.5
- Upper Bound: 57.5 + 6.5 = 64.0
Therefore, 68% of the students received scores between 51.0 and 64.0.
Select the correct answer from each drop-down menu:
- The scores of eighth-grade students in a math test are normally distributed with a mean of 57.5 and a standard deviation of 6.5. From this data, we can conclude that [tex]$68\%$[/tex] of the students received scores between [tex]$51.0$[/tex] and [tex]$64.0$[/tex].
