You can use technology to simulate experiments with large numbers of trials.
See solution.
Practice makes perfect
We are told that 30 % of all new wooden benches have a patch of chipped paint. We want to find how closely can 100 random samples of 10 benches estimate this percent. First, let's see that we can use technology to simulate experiments with large numbers of trials. Here are the parameters of our simulation.
We are told that the actual percentage of new wooden benches that have a patch of chipped paint is 30 %.
The number of samples is 100.
The sample size, which is the number of benches in each sample, is 10.
Now, we can use this information to run our simulation. The result is a graph showing the frequencies of each sample percentage — the percent of chipped benches in the sample. The higher the bar, the more frequent the sample percentage.
We see that the sample percentages are clustered around 0.3 = 30 %. Also, the majority of the estimates are between 15 % and 45 %, which means that most of the samples are within 15 % of the actual percentage.
30 % - 15 % &= 15 %
30 % + 15 % &=45 %
Note that this just a sample solution. In general, the results of a simulation are different each time we run it, which is why the estimates may also vary.
