Case Study: Chest Sizes of Scottish Militiamen.

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.

“The associated normal curve is the one whose parameters are the same as the mean and standard deviation of the variable…” (Weiss, pg. 256). Thus the parameters used to find the normal curve for chest circumferences are µ = 39.85 and σ = 2.07.

c.) Use the table on page 254 to find the percentage of militiamen in the survey with chest circumference between 36 and 41 inches, inclusive. Note: as the circumference 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.

In order to find the percentage of militiamen with chest circumferences between 36 and 41 inches, we must add the frequency of these variables, and then divide by the total observations.

189+409+753+1062+1082+935=4430
4430/5732 = .7729

77.29%

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).

By utilizing the parameters for the normal curve, µ = 39.85 and σ = 2.07, we can obtain an approximation to the percentage of militiamen within the survey with chest circumferences between 35.5 and 41.5 inches.

First we will solve for standardized version of x or the standardized variable corresponding to x. (Weiss, pg. 258).

Z = ( x - µ ) / σ