Case Study - Chest Sizes of Scottish Militiamen
We presented a frequency distribution for data on chest circumference, in inches, for 5732 Scottish militiamen. As mentioned there, Adolphe Quetelet used a procedure for fitting a normal curve to the data based on the binomial distribution. Here you are to accomplish that task by using techniques that you studied in this chapter.
a. Construct a relative-frequency histogram for the chest circumference data, using classes based on a single value.
b. The population mean and population standard deviation of the chest circumferences are 39.85 and 2.07, respectively. Identify the normal curve that should be used for the chest circumferences.
c. Use the table on page 263 to find the percentage of militiamen in the survey with chest circumference between 36 and 41 inches. inclusive. 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.
d. 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 found in part (c).