# Chapter 6 - Normal Probability Distributions - 6-5 The Central Limit Theorem - Basic Skills and Concepts: 6

a) 0.1587. b)0.3632.

#### Work Step by Step

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 $\frac{\sigma}{\sqrt n}$. $z=\frac{value-mean}{standard \ deviation}=\frac{205.0-205.5}{\frac{8.6}{\sqrt{36}}}=-0.35.$ Using the table, the value belonging to scores less than -0.35: 0.3632.

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