Question

a professional pool player claims that she sinks at least one ball in a pocket on 80% of her opening break shots. in a recent set of 20 games, she sunk at least one ball on her break shot in only 14 of the games. a simulation of 100 trials was conducted to see how unusual these most recent games are. based on the dotplot of the simulation results and the pool players last 20 games, which conclusion can be drawn? the players true probability of sinking at least one ball on her break is 27%. another 100 simulated trials would show a much different outcome; therefore, we cannot draw any conclusions. it is most likely that she would sink at least one ball during her break exactly 16 times. there is about a 27% chance of her sinking at least one ball on her break 14 or fewer times in 20 games. this result is not unusual and there is no convincing evidence that her average is less than 80%.

Explanation:

• The first option is incorrect because the dot - plot is about the probability of getting 14 or fewer successes (sinking at least one ball) in 20 trials, not the true probability of sinking a ball.
• The second option is incorrect. While another 100 trials might have some variation, we can still draw conclusions from the current data.
• The third option is incorrect. The dot - plot shows a distribution of possible outcomes, not that the most likely outcome is exactly 16.
• The fourth option is correct. We count the number of dots (simulation trials) at 14 or fewer. If there are 27 dots (for example, if 27 out of 100 trials have 14 or fewer successes), then there is about a 27% chance of getting 14 or fewer successes. Since this is not an extremely low probability (commonly, probabilities above 5% are not considered highly unusual in basic statistical inference), there is no convincing evidence that her average (80% claim) is wrong.

Answer:

The fourth option: There is about a 27% chance of her sinking at least one ball on her break 14 or fewer times in 20 games. This result is not unusual and there is no convincing evidence that her average is less than 80%.