Question

mason is comparing his scores at three different golf courses. in golf, the goal is to have the lowest score out of the players. louisiana links has an average score of 97 with a standard deviation of 5. mason’s score was 91. fairfax fairways has an average score of 83 with a standard deviation of 7. mason’s score was 77. calabasas clubs has an average score of 102 with a standard deviation of 10. mason’s score was 93. at which course was mason’s score the most impressive when compared with the average? at which course was mason’s score the least impressive when compared with the average? use z - scores to answer the question. mason’s score was the most impressive at dropdown and the least impressive at dropdown.

Explanation:

Step1: Recall z - score formula

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x$ is the individual score, $\mu$ is the mean (average) score, and $\sigma$ is the standard deviation.

Step2: Calculate z - score for Louisiana Links

For Louisiana Links: $\mu = 97$, $\sigma = 5$, $x = 91$.
$z=\frac{91 - 97}{5}=\frac{- 6}{5}=-1.2$

Step3: Calculate z - score for Fairfax Fairways

For Fairfax Fairways: $\mu = 83$, $\sigma = 7$, $x = 77$.
$z=\frac{77 - 83}{7}=\frac{-6}{7}\approx - 0.86$

Step4: Calculate z - score for Calabassas Clubs

For Calabassas Clubs: $\mu = 102$, $\sigma = 10$, $x = 93$.
$z=\frac{93 - 102}{10}=\frac{-9}{10}=-0.9$

Step5: Compare z - scores

The more negative the z - score, the better (more impressive) the score is relative to the average, because a lower z - score means the score is further below the mean.
Among - 1.2, - 0.86, and - 0.9, - 1.2 is the most negative (Louisiana Links), and - 0.86 is the least negative (Fairfax Fairways).

Answer:

Mason’s score was the most impressive at Louisiana Links and the least impressive at Fairfax Fairways.