CASE STUDY

Chest Sizes of Scottish Militiamen

In 1817 , an article entitled "Statement of the Sizes of Men in Different Counties of Scotland, Taken from the Local Militia" appeared in the Edinburgh Medical and Surgical Journal Nol. 13, pp. 260-264). Included in the article were data on chest circumference for 5732 Scottish militiamen. The data were collected by an army contractor who was responsible for providing clothing for the militia. A frequency distribution for the chest circumferences, in inches, is given in the following table.

As mentioned, Adolphe Quetelet used a procedure for fitting a normal curve to the data. In the following questions, you are to accomplish that task by using techniques that you studied this week.

1. Construct a relative-frequency histogram for the chest circumferences data, using classes based on a single value.
2. The population mean and population standard deviation of the chest circumferences are 39.85 and 2.07, respectively. Draw a normal curve with these values reflected.
3. Find the percentage of militiamen in the survey with chest circumferences between 36 and 41 inches. Note: As the circumferences were rounded to the nearest inch, you are actually finding the percentage of militiamen in the survey with chest circumference between 35.5 and 41.5 inches.
4. Use the normal curve you identified in part (b) to obtain an approximation to the percentage of militiamen in the survey with chest circumference between 35.5 and 41.5 inches. Compare your answer to the exact percentage in part (c).
5. This week, we learned about normal distributions and z-score. Are there any applications from this week’s content to your major, your profession, or your interests? Please explain.

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