## Elementary Statistics (12th Edition)

The highest weight before the diet: 212. $\overline{d}$ is the averages of the differences, hence: $\overline{d}=\frac{183+212+177+208+155+162+167+170}{8}=179.25.$ $s_d$ is the standard deviation of the differences, hence$s_d=\sqrt{\frac{\sum (x-\mu)^2}{n-1}}=\sqrt{\frac{(183-179.25)^2+...+(170-179.25)^2}{7}}=20.8378.$ $z=\frac{value-mean}{standard \ deviation}=\frac{212-179.25}{20.8378}=1.57$.