Answer:
Explained below.
Step-by-step explanation:
The scores turned in by an amateur golfer at the Bonita Fairways Golf Course in Bonita Springs, Florida are,
Season 1: {75, 79, 80, 78, 76, 74, 76, 78}
Season 2: {72, 71, 76, 78, 86, 81, 72, 80}
(a)
Compute the mean and standard deviation of the golfer's scores as follows:
Season 1:
[tex]\bar x_{1}=\frac{1}{n_{1}}\sum x_{1}\\\\=\frac{1}{8}\times 616\\\\=77[/tex]
[tex]s_{1}=\sqrt{\frac{1}{n-1}\sum(x_{1}-\bar x_{1})^{2}}\\\\=\sqrt{\frac{1}{8-1}\times 30}\\\\=2.0702\\\\\approx 2.07[/tex]
Season 2:
[tex]\bar x_{2}=\frac{1}{n_{2}}\sum x_{2}\\\\=\frac{1}{8}\times 616\\\\=77[/tex]
[tex]s_{2}=\sqrt{\frac{1}{n_{2}-1}\sum(x_{2}-\bar x_{2})^{2}}\\\\=\sqrt{\frac{1}{8-1}\times 194}\\\\=5.26444\\\\\approx 5.26[/tex]
(b)
The primary difference in performance between the two seasons is:
[tex]\text{Diff} = \bar x_{2}-\bar x_{1}\\\\=5.26-2.07\\\\=3.19[/tex]
