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 louisiana links, fairfax fairways, calabasas clubs (select from the box) and the least impressive at (select from the box).

Explanation:

Step1: Recall z - score formula

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x$ is the individual's score, $\mu$ is the mean (average) score, and $\sigma$ is the standard deviation. A lower z - score (more negative) indicates a score that is more below the mean, and a higher z - score (less negative or positive) indicates a score that is closer to or above the mean. For golf, a lower score is better, so we want to find the z - scores for each course.

Step2: Calculate z - score for Louisiana Links

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

Step3: Calculate z - score for Fairfax Fairways

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

Step4: Calculate z - score for Calabasas Clubs

For Calabasas Clubs: $\mu = 102$, $x = 93$, $\sigma=10$.
Using the z - score formula: $z=\frac{93 - 102}{10}=\frac{-9}{10}=-0.9$

Now, we compare the z - scores: $-1.2<-0.9<-0.86$. The most negative z - score is for Louisiana Links (which means his score is the most below the mean, so most impressive in golf as lower score is better), and the least negative (closest to the mean) is for Fairfax Fairways (so least impressive as his score is closest to the mean, relatively higher compared to the other courses' performance relative to the mean).

Answer:

Most impressive at: Louisiana Links; Least impressive at: Fairfax Fairways