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Use the information in the table to complete the statements.

| Age | Mean | Standard Deviation |
|-----------|---------|---------------------|
| 12 years | 58 inches | 2.3 inches |

1. About 68% of sixth-grade students will have heights between 55.7 inches and ______ inches.
2. About 95% of sixth-grade students will have heights between ______ inches and ______ inches.

Sagot :

GinnyAnswer
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.
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