[tex]\begin{gathered} \operatorname{mean}\text{ = }\mu=177 \\ s\tan dart\text{ }deviation\text{ = }\sigma=7.4 \\ \text{Emperical rule for }68\text{\%} \\ heights=\mu\pm1\cdot\sigma \\ heights=177\pm1\cdot(7.4) \\ \text{height1 = 177+7.4=184.4} \\ height\text{ 2 =177-7.4=169.6} \\ 68\text{\% of the data } \\ 169.6\operatorname{cm}--184.4\operatorname{cm} \\ \text{Emperical rule for }95\text{\%} \\ heights=\mu\pm2\cdot\sigma \\ \text{heights}=177\pm2\cdot(7.4) \\ \text{height1 = 177+14.8=1}91.8 \\ \text{height2 = 177-14.8=162.2} \\ 95\text{\% of the data } \\ 162.2cm--191.8\operatorname{cm} \\ \text{Emperical rule for }99.7\text{\%} \\ heights=\mu\pm3\cdot\sigma \\ \text{heights}=177\pm3\cdot(7.4) \\ \text{height1 =177+22.2=1}99.2 \\ \text{height2 =}177-22.2=154.8 \\ 99.7\text{\% of the data } \\ 154.8\operatorname{cm}--199.2\operatorname{cm} \end{gathered}[/tex]
