Chapter 7, Problem 27SE

ESP A Zener deck of cards has cards that show one of five different shapes with equal representation, so that the probability of selecting any particular shape is $\mathrm{0.20.}$ A card is selected randomly, and a person is asked to guess which card has been chosen. The graph below shows a computer simulation of experiments in which a “person” was asked to guess which card had been selected for a large number of trials. (If the person does not have ESP, then his or her proportion of successes should be about $0.20,$ give or take some amount.) Each dot in the dotplots represents the proportion of success for one person. For instance, the dot in Figure A farthest to the right represents a person with an $80\%$ success rate. One dotplot represents an experiment in which each person had 10 trials; another shows 20 trials; and a third shows 40 trials.

Explain how you can tell, from the widths of the graphs, which has the largest sample $\left(n=40\right)$ and which has the smallest sample $\left(n=10\right)$.