On page 263, 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 ap-proximation 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)

6.1 Introducing Normally Distributed Variables 263 Chest size (in.) |Frequency Chest size (in.) |Frequency 33 3 41 935 34 19 42 646 35 81 43 313 36 189 44 168 37 409 45 50 38 753 46 18 39 1062 47 3 40 1082 48 In his book Lettres a S.A.R. le Duc (a special type of bell-shaped curve) Regnant de Saxe-Cobourg et Gotha to the data on chest circumference. sur la theorie des probabilites At the end of this chapter, you will appliquee aux sciences morales et be asked to fit a normal curve to the politiques (Brussels: Hayez, 1846), data, using a technique different Adolphe Quetelet discussed a from the one used by Quetelet. procedure for fitting a normal curve