Answer: About 99.7% of sixth-grade students will have
heights between 51.1 inches and 64.9 inches.
Step-by-step explanation:
According to the empirical rule, 99.7% of data falls within the three standard deviations from the mean.
Given : Mean: [tex]\mu=58\text{ inches}[/tex]
Standard deviation:= [tex]\sigma=2.3\text{ inches}[/tex]
Then, the 99.7% of sixth-grade students will have heights between
[tex]\mu-3\sigma[/tex] inches and [tex]\mu+3\sigma[/tex] inches
i.e. [tex]58-3(2.3)[/tex] inches and [tex]58+3(2.3)[/tex] inches
i.e. 51.1 inches and 64.9 inches.
