Below is a simulation of the "fruit bearing" qualities of three strains of fruit trees.
This simulation was suggested by the questionable example from the
textbook. In that example, data suggested that in all cases, 95% of the fruit trees planted produced fruit.
That is unreasonable. After all, 95% is 19/20 so it can only work on multiples of 20 trees planted.
It certainly would not be possible to achieve if 107 trees are planted. Furthermore,
there should be an expectation that there is some variablility in each group planted.
To demonstrate this variability, the simulation below presents three different strains of trees, each of
which should have, on the average, 95% of the planted trees bearing fruit. The simulation
allows the user to plant 50 groves of trees at a time for each strain. Each grove has 100 trees.
The program keeps track of the number of fruit-bearing trees that come from each grove, as well as
the total number of fruit-bearing trees. The output for each strain shows the average
of all trees planted for the strain, as well as the distribution of the the number of fruit-bearing
trees in each grove.
As in any simulation, the results will be different each time this program is run. However,
the overall trends should be the same. That is, the averages should approximate 95% and the
distribution of any one strain should be similar from one run to the next. The more groves planted,
the more the true nature of each strain should be apparent.