## Elementary Statistics (12th Edition)

a) $z=\frac{value-mean}{standard \ deviation}=\frac{222.7-205.5}{8.6}=2.$ Using the table, the value belonging to 2: 0.9772. b) By using the Central Limit Theorem, the sample mean has a mean of $\mu$ and standard deviation of $\frac{\sigma}{\sqrt n}$. $z=\frac{value-mean}{standard \ deviation}=\frac{207-205.5}{\frac{8.6}{\sqrt{49}}}=1.22.$ Using the table, the value belonging to scores less than 1.22: 0.8888.