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Just How Normal Are You?

Resources for this lesson:

You will use your Algebra II Journal opens in new window on this page.

> Glossary opens in new window
> Calculator Resources opens in new window
> Teacher Resources: Instructional Notes opens in new window

Andrew and Khalid are discussing what they have learned so far about the presidents.

andrewAndrew: We have looked at the presidents’ ages and their heights. We have looked at how long the presidents have served. What haven’t we studied about the presidents?

andrewKhalid: Well, we haven’t looked at the presidents’ weight!


The table below displays the weights of the presidents.

President

Weight (pounds)

1. G. Washington

175

2. J. Adams

150

3. T. Jefferson

174

4. J. Madison

100

5. J. Monroe

189

6. J. Q. Adams

174

7. A. Jackson

140

8. M. Van Buren

173

9. W. H. Harrison

139

10. J. Tyler

141

11. J. Polk

174

12. Z. Taylor

170

13. M. Fillmore

164

14. F. Pierce

144

15. J. Buchanan

198

16. A. Lincoln

180

17. A. Johnson

174

18. U. Grant

156

19. R. Hayes

170

20. J. Garfield

184

21. C. Arthur

224

22. G. Cleveland

260

23. B. Harrison

150

24. G. Cleveland

260

25. W. McKinley

199

26. T. Roosevelt

210

27. W. H. Taft

316

28. W. Wilson

170

29. W. Harding

173

30. C. Coolidge

147

31. H. Hoover

187

32. F. D. Roosevelt

188

33. H. Truman

167

34. D. Eisenhower

171

35. J. F. Kennedy

173

36. L. Johnson

200

37. R. Nixon

175

38. G. Ford

190

39. J. Carter

160

40. R. Reagan

185

41. G. H. Bush

196

42. W. Clinton

223

43. G. W. Bush

191

44. B. Obama

180

Check Your Understanding

Use the graphing calculator to construct a histogram of the data. Shown below is a suggested WINDOW to use for graphing the histogram in the calculator. Remember to use President Cleveland’s weight only once.

A calculator screen shot displaying the dimensions of the intended graphing window. Xmin equals 100, Xmax equals 340, Xscale equals 20, Ymin equals negative two, Ymax equals 25, Yscale equals 1, and Xresolution equals 1.

Check Your Understanding

Show AnswerHide Answer


Use the mean and standard deviation you calculated to sketch the normal curve for this normal distribution. (You may use the features of the graphing calculator to construct a normal distribution for this data if you feel comfortable with the calculator’s features. Be sure to adjust your window appropriately.)

Displayed here is a screen shot from the graphing calculator. Shown is the command to give the calculator in order to graph the normal curve. It states Y sub one equals normal PDF parenthesis x comma 179.1627907 comma 33.708 parenthesis.

Displayed here is a calculator screen shot displaying the dimensions of the intended graphing window. Xmin equals zero, Xmax equals 340, Xscale equals 20, Ymin equals zero, Ymax equals .015, Yscale equals 1, and Xresolution equals 1.

Displayed here is a calculator screen shot of the resulting graph. The graph is distinctly a normal, symmetric, bell-shaped curve.

Check Your Understanding

Show AnswerHide Answer A bell shaped normal curve is shown. The x axis extends from 105 to 270, with the peak of the bell at 180. The x axis is labeled Weights of Presidents and the y axis is labeled Frequency.


Compare and contrast the normal distribution with the histogram.

Displayed is the histogram showing the weight of the presidents. The graph is skewed strongly to the right, with the majority of the data clustered to the left. Displayed is the graph of the distinctly a normal, symmetric, bell-shaped curve.

President’s Weights

Normal Distribution

What do you notice?

You should notice that the weights are most definitely not normally distributed! The weights of the heavier presidents, such as President Taft, skew the data to the right.

Shown is the histogram showing the weight of the presidents. The graph is skewed strongly to the right, with the majority of the data clustered to the left. A red curve has been drawn above the histogram to emphasize the strongly skewed nature of the graph

This data set is a reminder: While many data sets follow a normal distribution, many do not! As you continue your work with data distributions, mean and standard deviation, remember this important fact. Normal distributions are special, and not all data sets are normal.

Algebra II Journal: Reflection 3

In this lesson, you used the mean and standard deviation of a data set to fit the data to a normal distribution and to estimate percentages using the normal distribution.

Respond to the following reflection questions in your Algebra II Journal opens in new window and submit to your teacher.

  • Why are normal distributions important to statistics?
  • Why do some data sets follow normal distributions and some do not? Refer to the presidents’ weight data to support your answer.

 

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