An example of an early application of statistics was in the year 1817. A study of chest circumference among a group of Scottish men exhibited an approximately normal distribution. Their chest circumferences ranged from 33 to 48 inches, with a mean chest measurement of 40 inches and a standard deviation of 2 inches. Make a normal bell curve, then use the Empirical Rule to help you understand the distribution of chest circumferences in the study.

a) What range of chest measurements contains the 58% which fall closest to the mean?

b) What would you expect the chest measurements to be fore the 2.5% of the men with the smallest chest measurements?

c) What would you expect to be the smallest and largest chest measurements of the “middle” 95% of the men?

d) What would you expect to be the measurements of the 16% of the men with the largest chests in the population