Final answer:
Using the empirical rule, approximately 95% of elementary school students are expected to have heights between 95 cm and 115 cm if the heights are normally distributed with a mean of 105 cm and a standard deviation of 5 cm.
Step-by-step explanation:
To determine what percentage of elementary school students have heights between 95 cm and 115 cm given a normal distribution with a mean of 105 cm and a standard deviation of 5 cm, we can apply the empirical rule (also known as the 68-95-99.7 rule). According to this rule:
- Approximately 68% of the data falls within one standard deviation of the mean (100 cm to 110 cm).
- Approximately 95% falls within two standard deviations (95 cm to 115 cm).
- Approximately 99.7% falls within three standard deviations (90 cm to 120 cm).
Since the range from 95 cm to 115 cm encompasses two standard deviations from the mean, the percentage of students we would expect to have heights in this range is approximately 95%.
The correct answer to the student's question is b) 95%.