During the summer, T.J. participates in a Thursday night softball league.  Throughout the eight week season, he kept track of the number of times he struck out per game. Here is his data:

 week: 1 2 3 4 5 6 7 8 strikeouts: 4 2 5 3 7 4 5 2

1. Find his average (mean) number of strikeouts per game this season.
2. Find the standard deviation of the strikeout data.

T.J.'s girlfriend (with whom he's struck out many times as well) thinks he'd play better if he didn't drink beer right before the game.  Throughout the eight week season, she kept track of how many beers he consumed before playing. Here is her data:

 week: 1 2 3 4 5 6 7 8 # beers: 4 1 3 2 4 1 5 2

3. Let X equal the number of beers and let Y equal the number of strikeouts.  Find
the regression line Y = mX+b.
4. What is the correlation between beer consumption and strikeouts? (Numerically, we
mean. We know what your opinion is.)

T.J. has been demoted to manager.  He has to decide which 9 players (out of the 20 malcontents on the team) he wants for the game on Saturday.

5. How many different options does he have for making up a team?

Now that T.J. has chosen his team of nine players, he needs to decide the opening line-up of four players.

6. How many different line-ups are there for him to choose from?

The full line up consists of all nine players.

7. How many full line-ups are there?

Here are the solutions.

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