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Mathematics, 02.04.2021 06:00 Ruchen

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. A dotplot titled the professional pool player has number of games with at least one ball made on the break on the x-axis, and frequency on the y-axis. 10, 1; 12, 3; 13, 11; 14, 12; 15, 17; 16, 25; 17, 16; 18, 9; 19, 5; 20, 2.

Based on the dotplot of the simulation results and the pool player’s last 20 games, which conclusion can be drawn?

The player’s 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%.

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