EXAMPLE 1 Using a density curve

Figure 13.4 copies Figure 13.3, showing the histogram and the Normal density curve that describe this data set of 130 body temperatures. What proportion of the temperatures are greater than or equal to 99 degrees Fahrenheit? From the actual 130 observations, we can count that exactly 19 are greater than or equal to 99°F. So the proportion is 19/130, or 0.146. Because 99 is one of the break points between the classes in the histogram, the area of the shaded bars in Figure 13.4(a) makes up 0.146 of the total area of all the bars.

Now concentrate on the density curve drawn through the histogram. The total area under this curve is 1, and the shaded area in Figure 13.4(b) represents the proportion of observations that are greater than or equal to 99°F. This area is 0.1587. You can see that the density curve is a quite good approximation—0.1587 is close to 0.146.