Final answer:
The range of heights that includes approximately 99.7% of the students is 130 cm to 190 cm, according to the empirical rule for a normal distribution with a mean of 160 cm and a standard deviation of 10 cm. Option B is the correct answer.
Step-by-step explanation:
To determine the range of heights that includes approximately 99.7% of the students in this group, you can apply the empirical rule, sometimes referred to as the 68-95-99.7 rule. This rule states that for a normal distribution, about 68% of the data falls within one standard deviation of the mean, about 95% falls within two standard deviations, and about 99.7% falls within three standard deviations. Since the mean height is 160 cm and the standard deviation is 10 cm:
- One standard deviation from the mean ranges from 150 cm to 170 cm (which includes about 68% of the data).
- Two standard deviations from the mean ranges from 140 cm to 180 cm (which includes about 95% of the data).
- Three standard deviations from the mean ranges from 130 cm to 190 cm (which includes about 99.7% of the data).
Therefore, the range of heights that includes approximately 99.7% of the students is 130 cm to 190 cm, which corresponds to option (b).
The correct answer to the question, "What is the range of heights that includes approximately 99.7% of the students in this group?" is (b) 130 cm to 190 cm.