Solution Assignment 01 of the basics of statistics

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The 95% confidence interval of the mean \mu of a normally distributed population is [106.16; 109.84]. The population standard deviation \sigma is given and equals 20.2.

What has been the sample size? Explain your answer.

Solution.
The confidence interval is \displaystyle{\overline{x}\pm{z_{\alpha/2}}\frac{\sigma}{\sqrt{n}}}. From the given interval we may conclude that \overline{x}=108, right in the middle of the interval. So, \displaystyle{z_{\alpha/2}\frac{\sigma}{\sqrt{n}}. Furthermore, we know that z_{\alpha/2}=1.96 and \sigma=20.2. We find \displaystyle{n=(\frac{z_{\alpha/2}\sigma}{1.84})^2=463}.

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