192 Fundamentals of Statistics
The xy coordinate system on the target shows the bull’s eye, located at the
origin (0, 0). The distribution of the shots around the target is described by a
bivariate density function because it involves two random variables (one for
the vertical location and one for the horizontal location of each shot). We’ll
concentrate on the horizontal distribution of the shots.
Although many of the shots are near the bull’s eye, about a third of them
are farther than 0.4 horizontal unit away, either to the left or to the right
of the target. Because these are random data, your values may be different.
Based on the accuracy level you selected, a probability distribution show-
ing the expected distribution of shots to the left or right of the target is also
generated in the second column of the table. In this example, the predicted
proportion of shots within 0.4 unit of the target is 68.3%, which is close to
the observed value of 70%. In other words, the distribution predicts that a
person of moderate ability is able to hit the bull’s eye within 0.4 horizontal
unit about 68% of the time. This person came pretty close.
You can also examine the distribution of these shots by looking at the his-
togram of the shots. For the purposes of this worksheet, a shot to the left of
the target has a negative value and a shot to the right of the target has a posi-
tive value. The solid curve is the probability density function of shots to the
left or right of the target. After 50 shots, the histogram does not follow the
probability density function particularly closely. As you increase the num-
ber of shots taken, the distribution of the observed shots should approach
the predicted distribution.To increase the number of shots taken:1 Click the Shoot button again.
2 Click the Moderate button and click the spin arrow to increase the
number of shots to 500.Figure 5-7
Randomly
generated
sample
of shots