Questions: The table below shows the means and standard deviations for four of the variables in the NBAPlayers 2019 dataset. FGPct is the field goal percentage, Points is the total number of points scored during the season, Assists is the total number of assists during the season, and Steals is the total number of steals during the season. James Harden of the Houston Rockets was selected to the All-NBA First Team for his performance during this season. He had a field goal percentage of 0.442, scored 2818 points, had 586 assists, and had 158 steals. Variable Mean Standard Deviation FGPct 0.463 0.057 Points 981 478 Assists 219 148 Steals 63.5 31.2 Find the z-score for each of Harden's statistics. Round your answers to two decimal places. z-score for FGPct = z-score for Points =

The table below shows the means and standard deviations for four of the variables in the NBAPlayers 2019 dataset. FGPct is the field goal percentage, Points is the total number of points scored during the season, Assists is the total number of assists during the season, and Steals is the total number of steals during the season. James Harden of the Houston Rockets was selected to the All-NBA First Team for his performance during this season. He had a field goal percentage of 0.442, scored 2818 points, had 586 assists, and had 158 steals.

Variable Mean Standard Deviation
FGPct 0.463 0.057
Points 981 478
Assists 219 148
Steals 63.5 31.2

Find the z-score for each of Harden's statistics.
Round your answers to two decimal places.
z-score for FGPct =
z-score for Points =

Transcript text: The table below shows the means and standard deviations for four of the variables in the NBAPlayers 2019 dataset. FGPct is the field goal percentage, Points is total number of points scored during the season, Assists is total number of assists during the season, and Steals is total number of steals during the season. James Harden of the Houston Rockets was selected to the All-NBA First Team for his performance during this season. He had a field goal percentage of 0.442 , scored 2818 points, had 586 assists, and had 158 steals. \begin{tabular}{lcc} \hline Variable & Mean & \begin{tabular}{l} Standard \\ Deviation \end{tabular} \\ \hline FGPct & 0.463 & 0.057 \\ Points & 981 & 478 \\ Assists & 219 & 148 \\ Steals & 63.5 & 31.2 \\ \hline \end{tabular} Find the $z$-score for each of Harden's statistics. Round your answers to two decimal places. $z$-score for FGPct $=$ $\square$ z-score for Points =

Solution

Solution Steps

To find the $z$-score for each of Harden's statistics, we use the formula for the $z$-score: \[ z = \frac{(X - \mu)}{\sigma} \] where $ X $ is the value of the statistic, $ \mu $ is the mean of the statistic, and $ \sigma $ is the standard deviation of the statistic. We will calculate the $z$-score for each of the four statistics: FGPct, Points, Assists, and Steals.

Step 1: Calculate the $z$-score for FGPct

To find the $z$-score for Harden's field goal percentage (FGPct), we use the formula: \[ z = \frac{(X - \mu)}{\sigma} \] where $ X = 0.442 $, $ \mu = 0.463 $, and $ \sigma = 0.057 $.

\[ z_{\text{FGPct}} = \frac{(0.442 - 0.463)}{0.057} = -0.3684 \approx -0.37 \]

Step 2: Calculate the $z$-score for Points

To find the $z$-score for Harden's total points, we use the same formula: \[ z = \frac{(X - \mu)}{\sigma} \] where $ X = 2818 $, $ \mu = 981 $, and $ \sigma = 478 $.

\[ z_{\text{Points}} = \frac{(2818 - 981)}{478} = 3.8393 \approx 3.84 \]

Step 3: Calculate the $z$-score for Assists

To find the $z$-score for Harden's total assists, we use the same formula: \[ z = \frac{(X - \mu)}{\sigma} \] where $ X = 586 $, $ \mu = 219 $, and $ \sigma = 148 $.

\[ z_{\text{Assists}} = \frac{(586 - 219)}{148} = 2.4824 \approx 2.48 \]

Step 4: Calculate the $z$-score for Steals

To find the $z$-score for Harden's total steals, we use the same formula: \[ z = \frac{(X - \mu)}{\sigma} \] where $ X = 158 $, $ \mu = 63.5 $, and $ \sigma = 31.2 $.

\[ z_{\text{Steals}} = \frac{(158 - 63.5)}{31.2} = 3.0321 \approx 3.03 \]