use the information in the table to complete the statements.\n| age | mean | standard deviation |\n| ---- |…
use the information in the table to complete the statements.\n| age | mean | standard deviation |\n| ---- | ---- | ---- |\n| 12 years | 58 inches | 2.3 inches |\nabout 68% of sixth - grade students will have heights between 55.7 inches and 60.3 inches.\nabout 95% of sixth - grade students will have heights between inches and inches.
Answer
Explanation:
Step1: Recall the empirical rule for normal - distribution
In a normal distribution, about 95% of the data lies within 2 standard deviations of the mean.
Step2: Calculate the lower bound
The mean $\mu = 58$ inches and the standard deviation $\sigma=2.3$ inches. The lower bound is $\mu - 2\sigma=58-2\times2.3=58 - 4.6 = 53.4$ inches.
Step3: Calculate the upper bound
The upper bound is $\mu + 2\sigma=58 + 2\times2.3=58+4.6 = 62.6$ inches.
Answer:
53.4, 62.6