Essentials of Statistics (5th Edition)

a) $z=\frac{value-mean}{standard \ deviation}=\frac{196.9-205.5}{8.6}=-1.$ Using the table, the value belonging to scores less than -1: 0.1587. b) By using the Central Limit Theorem, the sample mean has a mean of $\mu$ and standard deviation of $\frac{\sigma}{\sqrt n}$. $z=\frac{value-mean}{standard \ deviation}=\frac{205.0-205.5}{\frac{8.6}{\sqrt{36}}}=-0.3488.$ Using the table, the value belonging to scores less than -0.3488: 0.3669.