Refer to the Baseball 2008 data, which reports information on the 30 Major League Baseball teams for the 2008 season. Set up a variable that divides the teams into two groups, those that had a winning season and those that did not. That is, create a variable to count the teams that won 81 games or more, and those that won 80 or less. Next create a new variable for attendance, using three categories: attendance less than 2.0 million, attendance of 2,0 million up to 3.0 million, and attendance of 3.0 million or more.

a. Create a table that shows the number of teams with a winning season versus those with a losing season by the three categories of attendance. If a team is selected at random, compute the following probabilities:

1. Having a winning season.

2. Having a winning season or attendance of more than 3.0 million.

3. Given attendance of more than 3.0 million, having a winning season.

4. Having a losing season and drawing less than 2.0 million.

b. Create a table that shows the number of teams that play on artificial surfaces and natural surfaces by winning and losing records. If a team is selected at random, compute the following probabilities:

1. Selecting a team with a home field that has a natural surface.

2. Is the likelihood of selecting a team with a winning record larger for teams with natural or artificial surfaces?

3. Having a winning record or playing on an artificial surface.

Answer:

Step 1 of 2:

(a)

We are asked to create a table that shows the number of teams with a winning season versus those with a losing season by the three categories of attendance.

From the given data we can create a table that shows the number of teams with a winning season versus those with a losing season by the three categories of attendance.

Team Result |
Attendance (in million) |
|||

Total |
||||

Winning |
6 |
8 |
4 |
18 |

Losing |
5 |
6 |
1 |
12 |

Total |
11 |
14 |
5 |
30 |

If a team is selected at random, compute the following probabilities:

- Having a winning season.

From the above table, we can see that the team has won total 18 games out of 30.

The probability

- Having a winning season or attendance of more than million.

We need to find

Using addition theorem of probability, we can write,

From the table, we can find the numbers,

- Given attendance of more than million, having a winning season.

We need to find

We know the conditional probability,

Hence we can write from the table,

- Having a losing season and drawing less than 2.0 million.

We need to find

We can write from the table,