# Case study: chest sizesof scottish militiamen

Case Study: Chest Sizesof Scottish Militiamen: Answer a,b,c,d. You must CALCULATE results by hand.

Chest circumference for 5732 militiamen. Data was collected by an army contractor who was responsible for providing clothing for militia. A frequency distribution for the chest circumferences in inches is given:

Chest size (in.) Frequency

33 3
34 19
35 81
36 189
37 409
38 753
39 1062
40 1082
41 935
42 646
43 313
44 168
45 50
46 18
47 3
48 1

AdolpheQuetelet used a procedure for fitting a normal curve to the data based on the binomial distribution. Accomplish this task using his technique.

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 to find percentage of militiamen with chest circumference between 36 and 41, inclusive. NOTE: as the circumference were rounded to the nearest inch, you are actually finding the percentage of militiamen 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 answers to the exact percentages found in part (c)