To solve this problem, we use the information provided in the table:
- Age: 12 years
- Mean Height: 58 inches
- Standard Deviation: 2.3 inches
We consider the following statistical ranges for normally distributed data based on the empirical rule:
1. 68% Data Range:
- This range includes the mean height plus or minus one standard deviation.
- Lower bound: [tex]\( \text{Mean Height} - 1 \times \text{Standard Deviation} = 58 - 2.3 = 55.7 \)[/tex] inches
- Upper bound: [tex]\( \text{Mean Height} + 1 \times \text{Standard Deviation} = 58 + 2.3 = 60.3 \)[/tex] inches
Therefore, about 68% of sixth-grade students will have heights between 55.7 inches and 60.3 inches.
2. 95% Data Range:
- This range includes the mean height plus or minus two standard deviations.
- Lower bound: [tex]\( \text{Mean Height} - 2 \times \text{Standard Deviation} = 58 - 2 \times 2.3 = 53.4 \)[/tex] inches
- Upper bound: [tex]\( \text{Mean Height} + 2 \times \text{Standard Deviation} = 58 + 2 \times 2.3 = 62.6 \)[/tex] inches
Therefore, about 95% of sixth-grade students will have heights between 53.4 inches and 62.6 inches.
So the completed statements are:
1. About 68% of sixth-grade students will have heights between 55.7 inches and 60.3 inches.
2. About 95% of sixth-grade students will have heights between 53.4 inches and 62.6 inches.
