Two players, Fredo and Karl, on different teams wanted to find out who scored the higher number of points when compared to the other players on his team.

Table 2.57
Player	His Average Points	Other's Average Points	Other's Standard Deviation
Fredo	 151
176
20

Karl	 151
175
35

Which player had the higher average points when compared to the other players on his team?

Fredo

Karl

Use Table 2.57 to find the value that is three standard deviations above the mean for each team.

Enter the exact answers.

Fredo's team:
Number
Karl's team:
Number

Use Table 2.57 to find the value that is three standard deviations below the mean for each team.

Enter the exact answers.

Fredo's team:
Number
Karl's team:
Number

To solve this problem, we will calculate the values that are three standard deviations above and below the mean for each player's team. Let's analyze the provided data from Table 2.57:

1. **Fredo's team:**
   - Fredo's average points: 151
   - Other players' average points: 176
   - Other players' standard deviation: 20

2. **Karl's team:**
   - Karl's average points: 151
   - Other players' average points: 175
   - Other players' standard deviation: 35

### Step-by-Step Calculations

#### 1. Three standard deviations above the mean

The formula to calculate the value that is three standard deviations above the mean is:

\[
\text{Value} = \text{Mean} + 3 \times \text{Standard Deviation}
\]

**For Fredo's team:**
\[
\text{Value} = 176 + 3 \times 20 = 176 + 60 = 236
\]

**For Karl's team:**
\[
\text{Value} = 175 + 3 \times 35 = 175 + 105 = 280
\]

#### 2. Three standard deviations below the mean

The formula to calculate the value that is three standard deviations below the mean is:

\[
\text{Value} = \text{Mean} - 3 \times \text{Standard Deviation}
\]

**For Fredo's team:**
\[
\text{Value} = 176 - 3 \times 20 = 176 - 60 = 116
\]

**For Karl's team:**
\[
\text{Value} = 175 - 3 \times 35 = 175 - 105 = 70
\]

### Final Answers

1. **Three standard deviations above the mean:**
   - Fredo's team: **236**
   - Karl's team: **280**

2. **Three standard deviations below the mean:**
   - Fredo's team: **116**
   - Karl's team: **70**

Would you like more details on any of these calculations or have any other questions?

Here are 5 related questions to expand your understanding:

1. What is the significance of calculating values three standard deviations above and below the mean?
2. How do standard deviations affect the spread of data?
3. Why might comparing individual player scores to their team's average be useful in a sports context?
4. How would you interpret a player's score if it is outside three standard deviations from the mean?
5. What other statistical measures could be useful in comparing player performances?

**Tip:** Understanding standard deviations helps in assessing how much variation exists within a dataset, which is critical for comparing performances relative to a group.

Learn how to calculate values that are three standard deviations above and below the mean using statistical data. This problem involves comparing player scores in a sports context and applying statistical concepts such as standard deviation.

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