SOLUTION
By the empirical rule, the 68% will lies between
[tex](\bar{x}-\sigma,\bar{x}+\sigma)[/tex]Where
[tex]\bar{x}=8.5\text{ and }\sigma=0.5[/tex]68% will lies between the interval
[tex]\begin{gathered} (8.5-0.5,8.5+0.5) \\ (8.0,9.0) \end{gathered}[/tex]For the percentage that lies between 7.5 and 9.5 we will have
[tex]\begin{gathered} 7.5=8.5-1=8.5-2(0.5)=\bar{x}-2\sigma \\ 9.5=8.5-1=8.5+2(0.5)=\bar{x}+2\sigma \end{gathered}[/tex]According to the empirical rule,
[tex]\text{ 95\% of the data falls in the interval }(7.5,9.5)[/tex]Therefore 95% will lies between 7.5 and 9.7 pounds
For the percentage that lies between 7 and 10 we will have
[tex]\begin{gathered} 7=8.5-1.5=8.5-3(0.5)=\bar{x}-3\sigma \\ 10=8.5+1.5=8.5+3(0.5)=\bar{x}+3\sigma \end{gathered}[/tex]According to the empirical rule,
[tex]\text{ 99.7\% of the data falls in the interval }(7,10)[/tex]Therefore 99.7% lies between 7 and 10 pounds
