# Empirical rule to test for normality

**Question description**

**Question 1**

Using the telephone numbers listed in your local directory as your population, randomly obtain 20 samples of size 3. From each telephone number identified as a source, take the fourth, fifth, and sixth digits.

- Calculate the mean of the 20 samples.
- Draw a histogram showing the 20 sample means. (Use classes -0.5 to 0.5, 0.5 to 1.5, and 1.5 to 2.5 and so on).
- Describe the distribution of the x-bars that you see in part b (shape of distribution, center, and the amount of dispersion).
- Draw 20 more samples and add the 20 new x-bars to the histogram in part b. describe the distribution that seems to be developing.

Use the empirical rule to test for normality. See the sampling distribution of sample means and the central limit theorem develop from your own data!

**Question 2**

Consider a population with μ = 43 and σ = 5.2.

- Calculate the z-score for anx̅ of 46.5 from a sample of size 35.
- Could this z-score be used in calculating probabilities using Table 3 in Appendix B? Why or why not?

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