Answered

Explore Westonci.ca, the top Q&A platform where your questions are answered by professionals and enthusiasts alike. Discover comprehensive answers to your questions from knowledgeable professionals on our user-friendly platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

The mean game scores and standard deviations of four seasons of a football team are given below.

\begin{tabular}{|c|c|c|}
\hline
Season & Mean & Standard Deviation \\
\hline
2005 & 19 & 3.5 \\
\hline
2006 & 21 & 2.8 \\
\hline
2007 & 12 & 1.0 \\
\hline
2008 & 9 & 4.0 \\
\hline
\end{tabular}

Which statement must be true?

A. The game scores of season 2006 have a greater spread than the game scores of season 2008.

B. The game scores of season 2007 have a greater spread than the game scores of season 2005.

C. The game scores of season 2006 have a greater spread than the game scores of season 2005.

D. The game scores of season 2005 have a greater spread than the game scores of season 2006.

Sagot :

GinnyAnswer
Let's analyze the standard deviations provided in the question to determine which statement is true:

1. Season 2005: Standard Deviation = 3.5
2. Season 2006: Standard Deviation = 2.8
3. Season 2007: Standard Deviation = 1.0
4. Season 2008: Standard Deviation = 4.0

Review the statements one by one in terms of standard deviations:

1. The game scores of season 2006 have a greater spread than the game scores of season 2008.
- Comparing standard deviations: \( 2.8 \) (2006) vs \( 4.0 \) (2008)
- Since \( 2.8 < 4.0 \), this statement is false.

2. The game scores of season 2007 have a greater spread than the game scores of season 2005.
- Comparing standard deviations: \( 1.0 \) (2007) vs \( 3.5 \) (2005)
- Since \( 1.0 < 3.5 \), this statement is false.

3. The game scores of season 2006 have a greater spread than the game scores of season 2005.
- Comparing standard deviations: \( 2.8 \) (2006) vs \( 3.5 \) (2005)
- Since \( 2.8 < 3.5 \), this statement is false.

4. The game scores of season 2005 have a greater spread than the game scores of season 2006.
- Comparing standard deviations: \( 3.5 \) (2005) vs \( 2.8 \) (2006)
- Since \( 3.5 > 2.8 \), this statement is true.

Therefore, the only true statement is:

The game scores of season 2005 have a greater spread than the game scores of season 2006.
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.