To determine the range in which approximately 68% of sixth-grade students' heights will fall, we can use the provided mean and standard deviation values. The mean (average height) is 58 inches, and the standard deviation (a measure of how spread out the heights are) is 2.3 inches.
In a normal distribution, about 68% of the data falls within one standard deviation from the mean. This means we need to calculate the range that is one standard deviation below the mean and one standard deviation above the mean.
1. Calculate the lower bound:
- Mean height: 58 inches
- Standard deviation: 2.3 inches
- Lower bound = Mean height - Standard deviation = 58 inches - 2.3 inches = 55.7 inches
2. Calculate the upper bound:
- Mean height: 58 inches
- Standard deviation: 2.3 inches
- Upper bound = Mean height + Standard deviation = 58 inches + 2.3 inches = 60.3 inches
Therefore, about 68% of sixth-grade students will have heights between 55.7 inches and 60.3 inches.
